A NOTE ON ZERO DIVISORS IN w-NOETHERIAN-LIKE RINGS

Title & Authors
A NOTE ON ZERO DIVISORS IN w-NOETHERIAN-LIKE RINGS
Kim, Hwankoo; Kwon, Tae In; Rhee, Min Surp;

Abstract
We introduce the concept of w-zero-divisor (w-ZD) rings and study its related rings. In particular it is shown that an integral domain R is an SM domain if and only if R is a w-locally Noetherian w-ZD ring and that a commutative ring R is w-Noetherian if and only if the polynomial ring in one indeterminate R[X] is a w-ZD ring. Finally we characterize universally zero divisor rings in terms of w-ZD modules.
Keywords
zero divisor;zero divisor ring;zero divisor module;universally zero divisor ring;w-operation;
Language
English
Cited by
1.
ON PIECEWISE NOETHERIAN DOMAINS,;;;

대한수학회지, 2016. vol.53. 3, pp.623-643
1.
ON PIECEWISE NOETHERIAN DOMAINS, Journal of the Korean Mathematical Society, 2016, 53, 3, 623
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