A note on zero divisors in $w$-Noetherian-like rings
Bull. Korean Math. Soc. 2014 Vol. 51, No. 6, 1851-1861
Printed November 30, 2014
Hwankoo Kim, Tae In Kwon, and Min Surp Rhee
Hoseo University, Changwon National University, Dankook University
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
MSC numbers : Primary 13A15; Secondary 13E99, 13F05
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