• Title, Summary, Keyword: universally zero divisor ring

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

  • Kim, Hwankoo;Kwon, Tae In;Rhee, Min Surp
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.6
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    • pp.1851-1861
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    • 2014
  • 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.