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

  • 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.

Keywords

zero divisor;zero divisor ring;zero divisor module;universally zero divisor ring;w-operation

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Cited by

  1. ON PIECEWISE NOETHERIAN DOMAINS vol.53, pp.3, 2016, https://doi.org/10.4134/JKMS.j150213

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)