×
Fontana, Marco

Topologically defined classes of commutative rings. (English) Zbl 0443.13001

Ann. Mat. Pura Appl., IV. Ser. 123, 331-355 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0443.13001

Cited in 3 Reviews
Cited in 179 Documents

MSC:

13B02 Extension theory of commutative rings
13A15 Ideals and multiplicative ideal theory in commutative rings
14A15 Schemes and morphisms

Keywords:

CPI-extensions; D+M constructions; glueings of prime

Citations:

Zbl 0363.13002
PDF BibTeX XML Cite
\textit{M. Fontana}, Ann. Mat. Pura Appl. (4) 123, 331--355 (1980; Zbl 0443.13001)
Full Text: DOI

References:

[1] S.Anantharaman,Schémas en groupes, espaces homogènes et espaces algébriques sur une base de dimension 1, Thèse, 1971. · Zbl 0286.14001
[2] Andreotti, A.; Bombieri, E., Sugli omeomorfismi delle varietà algebriche, Ann. Sc. Norm. Sup. Pisa, 23, 430-450 (1969) · Zbl 0184.24503
[3] Atiyah, M. F.; Macdonald, I. G., Introduction to commutative algebra (1969), Reading: Addison-Wesley, Reading
[4] Aull, C. E.; Thron, W. J., Separation axioms between T_0and T_1, Indag. Math., 24, 26-37 (1962) · Zbl 0108.35402
[5] Boisen, M. B.; Sheldon, P. B., CPI-extensions: overrings of integral domains with special prime spectrum, Canad. J. Math., 29, 722-737 (1977) · Zbl 0363.13002
[6] Bourbaki, N., Algèbre commutative (19611965), Paris: Hermann, Paris
[7] Bourbaki, N., Topologie générale (1971), Paris: Hermann, Paris
[8] A.Bouvier - M.Fontana,Une classe d’espaces spectraux de dimension 1:les espaces principaux, (à paraître). · Zbl 0459.13001
[9] Conte, A., Proprietà di separazione della topologia di Zariski di uno schema, Rend. Ist. Lombardo, A 106, 79-111 (1972) · Zbl 0254.14002
[10] J.Dieudonné,Topics in local algebra, Notre Dame Math. Lect. Notes, 1967. · Zbl 0193.00101
[11] Dobbs, D. E., On going down for simple overrings II, Comm. Algebra, 1, 439-458 (1974) · Zbl 0285.13001
[12] Dobbs, D. E.; Papick, I. J., On going down for simple overrings III, Proc. AMS, 54, 35-38 (1976) · Zbl 0285.13002
[13] Dugundji, J., Topology (1969), Boston: Allyn and Bacon, Boston
[14] Endô, S., Note on p.p. rings (a supplement to Hattori’s paper), Nagoya Math. J., 17, 167-170 (1960) · Zbl 0117.02203
[15] Endô, S., On semi-hereditary rings, J. Math. Soc. Japan, 13, 109-119 (1961) · Zbl 0102.02902
[16] Endô, S., Projective modules over polynomials rings, J. Math. Soc. Japan, 15, 339-395 (1963) · Zbl 0119.03504
[17] D.Ferrand,Conducteur, descente et pincement, Thèse.
[18] Fontana, M.; Maroscia, P., Sur les anneaux de Goldman, Boll. U.M.I., 13 B, 743-759 (1976) · Zbl 0351.13002
[19] Gilmer, R., Multiplicative ideal theory (1968), Kingston: Queen’s Univ. Press, Kingston
[20] Gilmer, R., A class of domains in which primary ideals are valuation ideals, Math. Ann., 161, 247-254 (1965) · Zbl 0135.08001
[21] Gilmer, R.; Bastida, E., Overrings and divisorial ideals of rings of the form D + M, Michigan Math. J., 20, 79-95 (1974) · Zbl 0239.13001
[22] Gilmer, R.; Heinzer, W. J., Intersections of quotient rings of an integral domain, J. Math. Kyoto Univ., 7, 133-150 (1967) · Zbl 0166.30601
[23] Grothendieck, A.; Dieudonne, J., Eléments de géométrie algébrique I (1971), Berlin: Springer, Berlin · Zbl 0203.23301
[24] Hochster, M., Prime ideal structure in commutative rings, Trans. AMS, 142, 46-60 (1969) · Zbl 0184.29401
[25] Kaplansky, I., Commutative rings (1970), Boston: Allyn and Bacon, Boston · Zbl 0203.34601
[26] Kikuchi, I., Some remarkes on S-domains, J. Math. Kyoto Univ., 6, 49-60 (1966) · Zbl 0158.03905
[27] Lewis, W. J., The spectrum of a rings as a partially ordered set, J. Algebra, 25, 419-434 (1973) · Zbl 0266.13010
[28] Lewis, W. J.; Ohm, J., The ordering of Spec R, Canad. J. Math., 28, 820-835 (1976) · Zbl 0313.13003
[29] P.Maroscia,Topological properties of some classes of G-domains, (to appear). · Zbl 0396.13019
[30] Nagata, M., Local rings (1962), New York: Interscience, New York
[31] Olivier, J. P., Anneaux absolument plats universels et épimorphismes d’anneaux, C. R. Acad. Sci. Paris, 266, A317-318 (1968) · Zbl 0157.08403
[32] Papick, I. J., Topologically defined classes of going-down domains, Trans. AMS, 219, 1-37 (1976) · Zbl 0345.13005
[33] Pedrini, C., Incollamenti di ideali primi e gruppi di Picard, Rend. Sem. Mat. Univ. Padova, 48, 39-66 (1973) · Zbl 0305.13005
[34] Pendleton, R. L., A characterization of Q-domains, Bull. AMS, 72, 499-500 (1966) · Zbl 0136.31405
[35] Picavet, G., Sur les anneaux commutatifs dont tout idéal premier est de Goldman, C. R. Acad. Sci. Paris, 280, A 1719-1721 (1975) · Zbl 0328.13001
[36] Ramaswamy, R.; Viswanathan, T. M., Overring properties of G-domains, Proc. AMS, 58, 59-66 (1976) · Zbl 0323.13003
[37] Tamone, G., Sugli incollamenti di ideali primi, Boll. U.M.I., 14 B, 810-825 (1977) · Zbl 0445.13001
[38] Traverso, C., Seminormality and Picard group, Ann. Sc. Norm. Sup. Pisa, 24, 585-595 (1970) · Zbl 0205.50501
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.