대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제51권6호
  • /
  • Pages.1851-1861
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  • 2014
  • /
  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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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)
  • 투고 : 2013.12.02
  • 발행 : 2014.11.30
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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.

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참고문헌

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피인용 문헌

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