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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Zero divisors in Noetherian-like rings

Author: E. Graham Evans
Journal: Trans. Amer. Math. Soc. 155 (1971), 505-512
MSC: Primary 13.50
MathSciNet review: 0272773
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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 [Enhancements On Off] (What's this?)

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Keywords: Noetherian rings, zero divisors, integral closure, polynomials, <IMG WIDTH="21" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$R$"> sequences, Serre subcategory, Laskerian, primary ideals, valuation rings
Article copyright: © Copyright 1971 American Mathematical Society