# zbMATH — the first resource for mathematics

## Northcott, Douglas Geoffrey

Compute Distance To:
 Author ID: northcott.douglas-geoffrey Published as: Northcott, D.; Northcott, D. G.
 Documents Indexed: 91 Publications since 1939, including 11 Books Biographic References: 1 Publication

#### Co-Authors

 80 single-authored 4 Eagon, John A. 4 Rees, David 2 Reufel, Manfred 1 Reutel, M.
all top 5

#### Serials

 18 Proceedings of the Cambridge Philosophical Society 12 Proceedings of the London Mathematical Society. Third Series 12 Journal of the London Mathematical Society 10 The Quarterly Journal of Mathematics. Oxford Second Series 4 Mathematika 3 Journal of the London Mathematical Society. Second Series 3 Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 3 Proceedings of the Glasgow Mathematical Association 2 Journal für die Reine und Angewandte Mathematik 2 Monatshefte für Mathematik 1 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Bulletin of the London Mathematical Society 1 Duke Mathematical Journal 1 Mathematische Annalen 1 Annals of Mathematics. Second Series 1 Cambridge Tracts in Mathematics 1 London Mathematical Society Lecture Note Series 1 Cambridge Tracts in Mathematics and Mathematical Physics
all top 5

#### Fields

 17 Commutative algebra (13-XX) 8 Category theory; homological algebra (18-XX) 4 Associative rings and algebras (16-XX) 3 History and biography (01-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 2 Algebraic geometry (14-XX) 2 Group theory and generalizations (20-XX)

#### Citations contained in zbMATH Open

63 Publications have been cited 1,343 times in 1,159 Documents Cited by Year
Reductions of ideals on local rings. Zbl 0057.02601
Northcott, D. G.; Rees, D.
1954
Lessons on rings, modules and multiplicities. Zbl 0159.33001
Northcott, D. G.
1968
Ideals defined by matrices and a certain complex associated with them. Zbl 0106.25603
Eagon, J. A.; Northcott, D. G.
1962
Finite free resolutions. Zbl 0328.13010
Northcott, D. G.
1976
An introduction to homological algebra. Zbl 0116.01401
Northcott, D. G.
1960
Ideal theory. Zbl 0052.26801
Northcott, D. G.
1953
A note on the coefficients of the abstract Hilbert function. Zbl 0118.04502
Northcott, D. G.
1960
Injective envelopes and inverse polynomials. Zbl 0284.13012
Northcott, D. G.
1974
Periodic points on an algebraic variety. Zbl 0036.30102
Northcott, D. G.
1950
A generalization of a theorem on the content of polynomials. Zbl 0103.27102
Northcott, D. G.
1959
A generalization of the concept of length. Zbl 0129.02203
Northcott, D. G.; Reufel, M.
1965
A further inequality in the theory of arithmetic on algebraic varieties. Zbl 0035.30701
Northcott, D. G.
1949
Some remarks on the theory of ideals defined by matrices. Zbl 0116.02504
Northcott, D. G.
1963
A homological investigation of a certain residual ideal. Zbl 0112.02904
Northcott, D. G.
1963
Generically acyclic complexes and generically perfect ideals. Zbl 0225.13004
Eagon, J. A.; Northcott, D. G.
1967
Principal systems. Zbl 0077.26001
Northcott, D. G.; Rees, D.
1957
On irreducible ideals in local rings. Zbl 0081.03402
Northcott, D. G.
1957
Affine sets and affine groups. Zbl 0424.20034
Northcott, D. G.
1980
On the notion of a first neighbourhood with an application to the $$AF+B\varPhi$$ theorem. Zbl 0082.03304
Northcott, D. G.
1957
A note on reductions of ideals with an application to the generalized Hilbert function. Zbl 0057.02602
Northcott, D. G.; Rees, D.
1954
On the Buchsbaum-Eisenbud theory of finite free resolutions. Zbl 0272.18010
Eagon, J. A.; Northcott, D. G.
1973
Generalized Koszul complexes and Artinian modules. Zbl 0241.18009
Northcott, D. G.
1972
A general theory of one-dimensional local rings. Zbl 0115.03304
Northcott, D. G.
1956
The neighbourhoods of a local ring. Zbl 0067.26803
Northcott, D. G.
1955
Multilinear algebra. Zbl 0543.15019
Northcott, D. G.
1984
A note on ideals which are saturated with respect to a specialization. Zbl 0106.25701
Northcott, D. G.
1962
Semi-regular rings and semi-regular ideals. Zbl 0112.03001
Northcott, D. G.
1960
A first course of homological algebra. Zbl 0302.18009
Northcott, D. G.
1973
Some inequalities between periodic functions and their derivatives. Zbl 0022.12405
Northcott, D. G.
1939
Grade sensitivity and generic perfection. Zbl 0196.06701
Northcott, D. G.
1970
Hilbert’s function in a local ring. Zbl 0050.03002
Northcott, D. G.
1953
Specializations over a local domain. Zbl 0044.26501
Northcott, D. G.
1951
A note on the Hilbert functions of certain ideals which are defined by matrices. Zbl 0108.04102
Eagon, J. A.; Northcott, D. G.
1962
An introduction to homological algebra. Reprint of the 1962 hardback ed. Zbl 1185.13002
Northcott, D. G.
2008
Duality and the theory of complexes. Zbl 0226.18008
Northcott, D. G.
1971
Additional properties of generically acyclic projective complexes. Zbl 0203.05301
Northcott, D. G.
1969
The centre of a hereditary local ring. Zbl 0101.27403
Northcott, D. G.
1962
Some contributions to the theory of one-dimensional local rings. Zbl 0098.26001
Northcott, D. G.
1958
Semi-regular local rings. Zbl 0074.02801
Northcott, D. G.
1956
Reduction of polynomial modules by means of an arbitrary valuation. Zbl 0127.26301
Northcott, D.; Reutel, M.
1965
The Hilbert function of the tensor product of two multigraded modules. Zbl 0122.04106
Northcott, D. G.
1963
Specialization of the isolated common zeros of a system of polynomial equations. Zbl 0109.26505
Northcott, D. G.
1962
Specialization of polynomial ideals and their zeros. Zbl 0109.02802
Northcott, D. G.
1962
On the homology theory of general commutative rings. Zbl 0103.26903
Northcott, D. G.
1961
The reduction number of a one-dimensional local ring. Zbl 0114.02302
Northcott, D. G.
1959
Extensions and simplifications of the theory of regular local rings. Zbl 0079.26601
Northcott, D. G.; Rees, D.
1957
Abstract dilatations and infinitely near points. Zbl 0074.02601
Northcott, D. G.
1956
On homogeneous ideals. Zbl 0064.26801
Northcott, D. G.
1955
On the local cone of a point on an algebraic variety. Zbl 0056.14503
Northcott, D. G.
1954
Multilinear algebra. Reprint of the 1984 hardback ed. Zbl 1185.15023
Northcott, D. G.
2008
Projective ideals and MacRae’s invariant. Zbl 0438.13006
Northcott, D. G.
1981
Topological groups and integral extensions. Zbl 0422.13008
Northcott, D. G.
1981
A first course of homological algebra. Zbl 0425.18015
Northcott, D. G.
1980
Syzygies and specializations. Zbl 0128.03302
Northcott, D. G.
1965
Prime ideals and Dedekind orders. Zbl 0204.05801
Northcott, D. G.
1960
An algebraic relation connected with the theory of curves on non-singular surfaces. Zbl 0087.35801
Northcott, D. G.
1959
A note on polynomial rings. Zbl 0081.26601
Northcott, D. G.
1958
On the algebraic foundations of the theory of local dilatations. Zbl 0072.38901
Northcott, D. G.
1956
A note on the $$AF+B\Phi$$ theorem and the theory of local rings. Zbl 0067.26901
Northcott, D. G.
1955
Some results concerning the local analytic branches of an algebraic variety. Zbl 0052.37903
Northcott, D. G.
1953
On unmixed ideals in regular local rings. Zbl 0050.26001
Northcott, D. G.
1953
The number of analytic branches of a variety. Zbl 0039.37401
Northcott, D. G.
1950
Some inequalities between periodic functions and their derivatives. JFM 65.0260.01
Northcott, D. G.
1939
An introduction to homological algebra. Reprint of the 1962 hardback ed. Zbl 1185.13002
Northcott, D. G.
2008
Multilinear algebra. Reprint of the 1984 hardback ed. Zbl 1185.15023
Northcott, D. G.
2008
Multilinear algebra. Zbl 0543.15019
Northcott, D. G.
1984
Projective ideals and MacRae’s invariant. Zbl 0438.13006
Northcott, D. G.
1981
Topological groups and integral extensions. Zbl 0422.13008
Northcott, D. G.
1981
Affine sets and affine groups. Zbl 0424.20034
Northcott, D. G.
1980
A first course of homological algebra. Zbl 0425.18015
Northcott, D. G.
1980
Finite free resolutions. Zbl 0328.13010
Northcott, D. G.
1976
Injective envelopes and inverse polynomials. Zbl 0284.13012
Northcott, D. G.
1974
On the Buchsbaum-Eisenbud theory of finite free resolutions. Zbl 0272.18010
Eagon, J. A.; Northcott, D. G.
1973
A first course of homological algebra. Zbl 0302.18009
Northcott, D. G.
1973
Generalized Koszul complexes and Artinian modules. Zbl 0241.18009
Northcott, D. G.
1972
Duality and the theory of complexes. Zbl 0226.18008
Northcott, D. G.
1971
Grade sensitivity and generic perfection. Zbl 0196.06701
Northcott, D. G.
1970
Additional properties of generically acyclic projective complexes. Zbl 0203.05301
Northcott, D. G.
1969
Lessons on rings, modules and multiplicities. Zbl 0159.33001
Northcott, D. G.
1968
Generically acyclic complexes and generically perfect ideals. Zbl 0225.13004
Eagon, J. A.; Northcott, D. G.
1967
A generalization of the concept of length. Zbl 0129.02203
Northcott, D. G.; Reufel, M.
1965
Reduction of polynomial modules by means of an arbitrary valuation. Zbl 0127.26301
Northcott, D.; Reutel, M.
1965
Syzygies and specializations. Zbl 0128.03302
Northcott, D. G.
1965
Some remarks on the theory of ideals defined by matrices. Zbl 0116.02504
Northcott, D. G.
1963
A homological investigation of a certain residual ideal. Zbl 0112.02904
Northcott, D. G.
1963
The Hilbert function of the tensor product of two multigraded modules. Zbl 0122.04106
Northcott, D. G.
1963
Ideals defined by matrices and a certain complex associated with them. Zbl 0106.25603
Eagon, J. A.; Northcott, D. G.
1962
A note on ideals which are saturated with respect to a specialization. Zbl 0106.25701
Northcott, D. G.
1962
A note on the Hilbert functions of certain ideals which are defined by matrices. Zbl 0108.04102
Eagon, J. A.; Northcott, D. G.
1962
The centre of a hereditary local ring. Zbl 0101.27403
Northcott, D. G.
1962
Specialization of the isolated common zeros of a system of polynomial equations. Zbl 0109.26505
Northcott, D. G.
1962
Specialization of polynomial ideals and their zeros. Zbl 0109.02802
Northcott, D. G.
1962
On the homology theory of general commutative rings. Zbl 0103.26903
Northcott, D. G.
1961
An introduction to homological algebra. Zbl 0116.01401
Northcott, D. G.
1960
A note on the coefficients of the abstract Hilbert function. Zbl 0118.04502
Northcott, D. G.
1960
Semi-regular rings and semi-regular ideals. Zbl 0112.03001
Northcott, D. G.
1960
Prime ideals and Dedekind orders. Zbl 0204.05801
Northcott, D. G.
1960
A generalization of a theorem on the content of polynomials. Zbl 0103.27102
Northcott, D. G.
1959
The reduction number of a one-dimensional local ring. Zbl 0114.02302
Northcott, D. G.
1959
An algebraic relation connected with the theory of curves on non-singular surfaces. Zbl 0087.35801
Northcott, D. G.
1959
Some contributions to the theory of one-dimensional local rings. Zbl 0098.26001
Northcott, D. G.
1958
A note on polynomial rings. Zbl 0081.26601
Northcott, D. G.
1958
Principal systems. Zbl 0077.26001
Northcott, D. G.; Rees, D.
1957
On irreducible ideals in local rings. Zbl 0081.03402
Northcott, D. G.
1957
On the notion of a first neighbourhood with an application to the $$AF+B\varPhi$$ theorem. Zbl 0082.03304
Northcott, D. G.
1957
Extensions and simplifications of the theory of regular local rings. Zbl 0079.26601
Northcott, D. G.; Rees, D.
1957
A general theory of one-dimensional local rings. Zbl 0115.03304
Northcott, D. G.
1956
Semi-regular local rings. Zbl 0074.02801
Northcott, D. G.
1956
Abstract dilatations and infinitely near points. Zbl 0074.02601
Northcott, D. G.
1956
On the algebraic foundations of the theory of local dilatations. Zbl 0072.38901
Northcott, D. G.
1956
The neighbourhoods of a local ring. Zbl 0067.26803
Northcott, D. G.
1955
On homogeneous ideals. Zbl 0064.26801
Northcott, D. G.
1955
A note on the $$AF+B\Phi$$ theorem and the theory of local rings. Zbl 0067.26901
Northcott, D. G.
1955
Reductions of ideals on local rings. Zbl 0057.02601
Northcott, D. G.; Rees, D.
1954
A note on reductions of ideals with an application to the generalized Hilbert function. Zbl 0057.02602
Northcott, D. G.; Rees, D.
1954
On the local cone of a point on an algebraic variety. Zbl 0056.14503
Northcott, D. G.
1954
Ideal theory. Zbl 0052.26801
Northcott, D. G.
1953
Hilbert’s function in a local ring. Zbl 0050.03002
Northcott, D. G.
1953
Some results concerning the local analytic branches of an algebraic variety. Zbl 0052.37903
Northcott, D. G.
1953
On unmixed ideals in regular local rings. Zbl 0050.26001
Northcott, D. G.
1953
Specializations over a local domain. Zbl 0044.26501
Northcott, D. G.
1951
Periodic points on an algebraic variety. Zbl 0036.30102
Northcott, D. G.
1950
The number of analytic branches of a variety. Zbl 0039.37401
Northcott, D. G.
1950
A further inequality in the theory of arithmetic on algebraic varieties. Zbl 0035.30701
Northcott, D. G.
1949
Some inequalities between periodic functions and their derivatives. Zbl 0022.12405
Northcott, D. G.
1939
Some inequalities between periodic functions and their derivatives. JFM 65.0260.01
Northcott, D. G.
1939
all top 5

#### Cited by 1,015 Authors

 24 Huneke, Craig L. 23 Vasconcelos, Wolmer V. 19 Sharp, Rodney Y. 19 Ulrich, Bernd 18 Goto, Shiro 17 Ratliff, Louis J. jun. 17 Verma, Jugal Kishore 16 Chang, Gyu Whan 12 Eisenbud, David 12 Rossi, Maria Evelina 11 Anderson, David Fenimore 11 Corso, Alberto 11 Kirby, David 10 Aberbach, Ian M. 10 Bruns, Winfried 10 Duong Quôc Việt 10 Hermida Alonso, José Angel 10 Herzog, Jürgen 9 Elias, Juan 9 Heinzer, William J. 9 Katz, Daniel 9 Le Truong, Hoang 9 Ngô Viêt Trung 9 Sahandi, Parviz 8 Buchsbaum, David A. 8 Hochster, Melvin 8 Polini, Claudia 8 Salce, Luigi 7 Giordano Bruno, Anna 7 Herrmann, Manfred 7 Lê Tuâń Hoa 7 Simis, Aron 7 Virili, Simone 7 Vogel, Wolfgang 6 Anderson, Daniel D. 6 Benedetto, Robert L. 6 Dikranjan, Dikran N. 6 Huckaba, Sam 6 Hyry, Eero 6 Mafi, Amir 6 Matsuoka, Naoyuki 6 O’Carroll, Liam 6 Picavet-L’Hermitte, Martine 6 Rush, David E. 6 Valla, Giuseppe 6 Weyman, Jerzy M. 5 D’Cruz, Clare 5 Guerrieri, Anna 5 Kustin, Andrew R. 5 Millevoi, Tomaso 5 Nguyen Tu Cuong 5 Northcott, Douglas Geoffrey 5 Orbanz, Ulrich 5 Ozeki, Kazuho 5 Park, Sangwon 5 Picavet, Gabriel 5 Planas-Vilanova, Francesc 5 Sally, Judith D. 5 Sánchez-Giralda, Tomás 5 Schenzel, Peter 5 Shah, Kishor 4 Asgharzadeh, Mohsen 4 Avramov, Luchezar L. 4 Barshay, Jacob 4 Bivià-Ausina, Carles 4 Brennan, Joseph Phillip 4 Buchweitz, Ragnar-Olaf 4 Carriegos, Miguel V. 4 Doyle, John R. 4 Enochs, Edgar E. 4 Epstein, Neil 4 Fouli, Louiza 4 Goodearl, Kenneth R. 4 Hashimoto, Mitsuyasu 4 Kabbaj, Salah-Eddine 4 Kleppe, Jan Oddvar 4 Kurihara, Masato 4 Lazard, Daniel 4 Lech, Christer 4 Marley, Thomas 4 Masuti, Shreedevi Kalyani 4 McAdam, Stephen J. 4 Miller, Matthew P. 4 Naghipour, Reza 4 Oh, Dong Yeol 4 Ooishi, Akira 4 Philippon, Patrice 4 Roberts, Joel L. 4 Samuels, Charles L. 4 Vetter, Udo 4 Vishkautsan, Solomon 4 Vraciu, Adela N. 4 Yuzvinsky, Sergey 4 Zaare-Nahandi, Rahim 3 Abhyankar, Shreeram Shankar 3 Achilles, Rüdiger 3 Bank, Bernd 3 Barucci, Valentina 3 Boda, Eduard 3 Böger, Erwin ...and 915 more Authors
all top 5

#### Cited in 167 Serials

 215 Journal of Algebra 83 Proceedings of the American Mathematical Society 76 Journal of Pure and Applied Algebra 66 Communications in Algebra 63 Transactions of the American Mathematical Society 48 Mathematische Zeitschrift 37 Mathematische Annalen 27 Manuscripta Mathematica 23 Mathematical Proceedings of the Cambridge Philosophical Society 20 Advances in Mathematics 19 Compositio Mathematica 17 Rendiconti del Seminario Matematico della Università di Padova 17 Linear Algebra and its Applications 16 Inventiones Mathematicae 16 Journal of Algebra and its Applications 15 Journal of Commutative Algebra 14 Archiv der Mathematik 14 Monatshefte für Mathematik 14 Nagoya Mathematical Journal 9 Duke Mathematical Journal 9 Glasgow Mathematical Journal 8 Israel Journal of Mathematics 8 Journal of Number Theory 8 Mathematika 8 Proceedings of the Edinburgh Mathematical Society. Series II 8 Journal of Symbolic Computation 7 Rocky Mountain Journal of Mathematics 7 Annales de l’Institut Fourier 7 Annali di Matematica Pura ed Applicata. Serie Quarta 7 Bulletin de la Société Mathématique de France 7 Mathematische Nachrichten 6 Bulletin of the Korean Mathematical Society 6 Forum Mathematicum 5 Linear and Multilinear Algebra 5 Acta Mathematica Vietnamica 5 Publications Mathématiques 5 Michigan Mathematical Journal 5 International Journal of Algebra and Computation 5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 Journal of Algebraic Combinatorics 5 Bulletin of the American Mathematical Society 4 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 4 Acta Arithmetica 4 Journal of Functional Analysis 4 Mathematica Slovaca 4 Tokyo Journal of Mathematics 4 Journal of the American Mathematical Society 3 Mathematical Notes 3 Arkiv för Matematik 3 Mathematics of Computation 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 3 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 3 Czechoslovak Mathematical Journal 3 Fuzzy Sets and Systems 3 Journal für die Reine und Angewandte Mathematik 3 Tohoku Mathematical Journal. Second Series 3 Bulletin of the American Mathematical Society. New Series 3 Applicable Algebra in Engineering, Communication and Computing 3 Algebra Colloquium 3 Journal of the European Mathematical Society (JEMS) 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Proceedings of the Japan Academy 2 Journal of Mathematical Analysis and Applications 2 Acta Mathematica 2 Algebra Universalis 2 Proceedings of the Japan Academy. Series A 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Rendiconti del Circolo Matemàtico di Palermo. Serie II 2 Semigroup Forum 2 Systems & Control Letters 2 Acta Mathematica Hungarica 2 Annals of Global Analysis and Geometry 2 Bulletin of the Iranian Mathematical Society 2 Computer Aided Geometric Design 2 Multidimensional Systems and Signal Processing 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Journal of Algebraic Geometry 2 Journal de Théorie des Nombres de Bordeaux 2 Turkish Journal of Mathematics 2 Mathematical Journal of Ibaraki University 2 Algebras and Representation Theory 2 Algebraic & Geometric Topology 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 International Journal of Number Theory 2 International Electronic Journal of Algebra (IEJA) 2 Asian-European Journal of Mathematics 2 Afrika Matematika 2 Arabian Journal of Mathematics 1 Acta Mechanica 1 Archive for History of Exact Sciences 1 Bulletin of the Australian Mathematical Society 1 Communications in Mathematical Physics 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Applied Mathematics and Mechanics 1 Periodica Mathematica Hungarica 1 Ukrainian Mathematical Journal 1 Beiträge zur Algebra und Geometrie ...and 67 more Serials
all top 5

#### Cited in 45 Fields

 754 Commutative algebra (13-XX) 257 Algebraic geometry (14-XX) 104 Associative rings and algebras (16-XX) 74 Number theory (11-XX) 62 Group theory and generalizations (20-XX) 48 Category theory; homological algebra (18-XX) 42 Dynamical systems and ergodic theory (37-XX) 41 Linear and multilinear algebra; matrix theory (15-XX) 37 Several complex variables and analytic spaces (32-XX) 26 Combinatorics (05-XX) 19 Order, lattices, ordered algebraic structures (06-XX) 16 Field theory and polynomials (12-XX) 16 Nonassociative rings and algebras (17-XX) 11 Functional analysis (46-XX) 11 Manifolds and cell complexes (57-XX) 11 Systems theory; control (93-XX) 10 Global analysis, analysis on manifolds (58-XX) 10 Computer science (68-XX) 9 Algebraic topology (55-XX) 7 Partial differential equations (35-XX) 7 Abstract harmonic analysis (43-XX) 7 Convex and discrete geometry (52-XX) 7 Differential geometry (53-XX) 6 Operator theory (47-XX) 5 Topological groups, Lie groups (22-XX) 5 Real functions (26-XX) 4 History and biography (01-XX) 4 Mathematical logic and foundations (03-XX) 4 $$K$$-theory (19-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 General topology (54-XX) 4 Mechanics of particles and systems (70-XX) 3 General algebraic systems (08-XX) 3 Functions of a complex variable (30-XX) 3 Ordinary differential equations (34-XX) 3 Geometry (51-XX) 3 Numerical analysis (65-XX) 3 Quantum theory (81-XX) 3 Information and communication theory, circuits (94-XX) 2 Approximations and expansions (41-XX) 2 Mechanics of deformable solids (74-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Measure and integration (28-XX) 1 Relativity and gravitational theory (83-XX)