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

김환구|이민섭|권태인
대한수학회 (The Korean Mathematical Society)|2014.11|대한수학회보 (Bulletin of the KMS)|제51권 제6호|pp. 1851-1861

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참고문헌

키워드

zero divisorzero divisor ringzero divisor moduleuniversally zero divisor ringw-operation
주제분류수학

초록

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.

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.

참고문헌 (22)

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