Zero divisors in Noetherian-like rings
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- by E. Graham Evans PDF
- Trans. Amer. Math. Soc. 155 (1971), 505-512 Request permission
Abstract:
The zero divisors of $R/I$ for every ideal $I$ of a Noetherian ring is a finite union of primes. We take this property as a definition and study the class of rings so defined. Such rings are stable under localization and quotients. They are not stable under integral closure and are highly unstable under polynomial adjunction. The length of maximal $R$ sequences is well defined on them. In this paper all rings are commutative with unit and all modules are unitary.References
- N. Bourbaki, Éléments de mathématique. Fascicule XXVIII. Algèbre commutative. Chapitre 3: Graduations, filtrations et topologies. Chapitre 4: Idéaux premiers associés et décomposition primaire, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1293, Hermann, Paris, 1961 (French). MR 0171800
- Irving Kaplansky, Commutative rings, Revised edition, University of Chicago Press, Chicago, Ill.-London, 1974. MR 0345945
- Irving Kaplansky, Commutative rings, Allyn and Bacon, Inc., Boston, Mass., 1970. MR 0254021
- Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0155856
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 155 (1971), 505-512
- MSC: Primary 13.50
- DOI: https://doi.org/10.1090/S0002-9947-1971-0272773-9
- MathSciNet review: 0272773