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

  • Kim, Hwankoo (School of Computer and Information Engineering Hoseo University) ;
  • Kwon, Tae In (Department of Mathematics Changwon National University) ;
  • Rhee, Min Surp (Department of Mathematics Dankook University)
  • Received : 2013.12.02
  • Published : 2014.11.30

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.

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

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