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Lazard, Daniel

Algèbre linéaire sur \(K[X_1,\dots,X_n]\) et élimination. (French) Zbl 0447.13008

Bull. Soc. Math. Fr. 105, 165-190 (1977).
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Cited in 3 Reviews
Cited in 41 Documents

MSC:

13F20 Polynomial rings and ideals; rings of integer-valued polynomials

Keywords:

syzygies; effectiveness; polynomial ring; algorithms for solving equations

Citations:

Zbl 0356.13007
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Full Text: DOI Numdam EuDML

References:

[1] BUSCHBAUM (D. A.) and EISENBUD (D.) . - Remarks on ideals and resolutions , ”Symposia Mathematica, Vol. 11”, p. 193-204. - London, New York, Academic Press, 1973 . MR 49 #2715 | Zbl 0294.13009 · Zbl 0294.13009
[2] BOURBAKI (N.) . - Algèbre commutative , chap. 1-7. - Paris, Hermann, 1961 - 1965 (Act. scient. et ind., 1290, 1293, 1308, 1314 ; Bourbaki 27, 28, 30 et 31).
[3] EAGON (J.) and NORTHCOTT (D.) . - Ideals defined by matrices and a certain complex associated to them , Proc. Royal Soc. of London, series A, t. 269, 1962 , p. 188-204. MR 26 #161 | Zbl 0106.25603 · Zbl 0106.25603 · doi:10.1098/rspa.1962.0170
[4] HERMANN (G.) . - Die Frage der entlich vielen Schritte in der Theorie der Polynomideale , Math. Annalen, t. 95, 1926 , p. 736-788. JFM 52.0127.01 · JFM 52.0127.01
[5] LAZARD (D.) . - Suites régulières dans les idéaux déterminantiels , Comm. in Algebra, t. 4, 1976 , p. 327-340. MR 53 #13197 | Zbl 0324.13011 · Zbl 0324.13011 · doi:10.1080/00927877608822110
[6] LAZARD (D.) . - Suites régulières dans les idéaux déterminantiels , II (à paraître) dans Comm. in Algebra). Zbl 0371.13011 · Zbl 0371.13011 · doi:10.1080/00927877808822239
[7] LAZARD (D.) . - Algèbre linéaire sur les anneaux de polynômes ”Comptes rendus des journées mathématiques S.M.F. [ 1974 Montpellier]” p. 365-368. - Montpellier Université des Sciences et Techniques du Languedoc 1974 (Cahiers mathématiques, 3).
[8] LAZARD (D.) . - Équations linéaires dans les anneaux de polynômes ”Colloque sur l’utilisation des calculateurs en mathématiques pures [ 1975 Limoges]”, p. 131-135 ; Bull. Soc. math. France, Mémoire 49-50 (à paraître). Numdam | MR 58 #5645 | Zbl 0371.13010 · Zbl 0371.13010
[9] LAZARD (D.) . - Algorithmes fondamentaux en algèbre commutative ”Journées algorithmiques [ 1975 , E.N.S., Paris]”, p. 131-138, Astérisque, 1976 , n^\circ 38-39. Zbl 0353.13002 · Zbl 0353.13002
[10] MACAULAY (F. S.) . - Algebraic theory of modular systems . - Cambridge, Cambridge University Press, 1916 ou New York, London, Stechert-Hafner, 1964 (Cambridge Tracts in Mathematics and mathematical Physics, 19). Zbl 0802.13001 · Zbl 0802.13001
[11] MUSSER (D. R.) . - Multivariate polynomial factorization , J. of A.C.M., t. 22, 1975 , p. 291-309. MR 53 #335a | Zbl 0301.65029 · Zbl 0301.65029 · doi:10.1145/321879.321890
[12] SEIDENBERG (A.) . - Construction in algebra Trans. Amer. math. Soc., t. 197, 1974 , p. 273-313. MR 50 #2141 | Zbl 0356.13007 · Zbl 0356.13007 · doi:10.2307/1996938
[13] VdW] VAN DER WAERDEN (B. L.) . - Moderne Algebra . Bände 1 und 2. - Berlin, J. Springer, 1930 - 1931 ; 3te verbesserte Auflage : Berlin, Springer-Verlag, 1950 - 1955 (Grundlehren der mathematischen Wissenschaften, 33-34) ; Translation from the 2nd German edition : New York, F. Ungar, 1950 - 1953 .
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