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Fibre products of Noetherian rings and their applications

Published online by Cambridge University Press:  24 October 2008

Tetsushi Ogoma
Tetsushi Ogoma
Affiliation:
Department of Mathematics, Faculty of Science, Kochi University, Kochi, 780, Japan
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Extract

The notion of fibre product in a category is quite basic and has been studied by many authors. Also in ring theory, it is known that the fibre product is useful in the construction of examples. (See for example [3], [4] and references of [1].) Unfortunately, most such examples are non-noetherian and so are unsatisfactory from the viewpoint of commutative algebra.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 2 , March 1985 , pp. 231 - 241
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Anderson, D. F. and Dobbs, D. E.. Pairs of rings with the same prime ideals. Canad. J. Math. 32 (1980), 362–384.CrossRefGoogle Scholar
[2]Eakin, P.. The converse to a well known theorem on Noetherian rings. Math. Ann. 177 (1968), 278–282.CrossRefGoogle Scholar
[3]Facchini, A.. Fibre products and Morita duality for commutative rings. Rend. Sent. Mat. Univ. Padova 67 (1981), 143–159.Google Scholar
[4]Fontana, M.. Topologically denned classes of commutative rings. Ann. Mat. Pura Appl. (4) 123 (1980), 331–355.CrossRefGoogle Scholar
[5]Grothendieck, A. and Dieudonné, J.. Éléments de Géométrie Algébrique, tome I, II, III, IV. (Publ. Math. I.H.E.S., 1960–1966.)CrossRefGoogle Scholar
[6]Hochester, M.. Topics in the homological theory of modules over commutative rings. C.B.M.S. Regional Conference Series in Math. no. 24, Amer. Math. Soc., Providence, (1975).CrossRefGoogle Scholar
[7]Matsumura, H.. Commutative Algebra (Benjamin, 1970).Google Scholar
[8]Nagata, M.. Local rings. (John Wiley, 1962).Google Scholar
[9]Nagata, M.. A type of subrings of a noetherian ring. J. Math. Kyoto Univ. 8 (1968), 465–467.Google Scholar
[10]Ogoma, T.. Non-catenary pseudo-geometric normal rings. Japan J. Math. 6 (1980), 147–163.CrossRefGoogle Scholar
[11]Ogoma, T.. Existence of dualizing complexes, to appear.Google Scholar
[12]Sharp, R. Y. (ed.). Commutative Algebra: Durham 1981, London Math. Soc, Lecture Notes Series no. 72 (Cambridge University Press 1982).Google Scholar
[13]Sharp, R. Y.. Cohen-Macaulay properties for balanced big Cohen-Macaulay modules. Math. Proc. Cambridge Philos. Soc. 90 (1981), 229–238.CrossRefGoogle Scholar
[14]Sharp, R. Y.. A cousin complex characterization of balanced big Cohen-Macaulay modules. Quart. J. Math. Oxford 33 (1982), 471–485.CrossRefGoogle Scholar
[15]Yanagihara, H.. On glueing of prime ideals. Hiroshima Math. J. 10 (1980), 351–363.CrossRefGoogle Scholar