Korean Journal of Mathematics

  • 제28권1호
  • /
  • Pages.65-73
  • /
  • 2020
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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ON WEAKLY LOCAL RINGS

  • Piao, Zhelin (Department of Mathematics, Yanbian University) ;
  • Ryu, Sung Ju (Department of Mathematics, Pusan National University) ;
  • Sung, Hyo Jin (Department of Mathematics, Pusan National University) ;
  • Yun, Sang Jo (Department of Mathematics, Dong-A University)
  • 투고 : 2019.10.07
  • 심사 : 2019.12.30
  • 발행 : 2020.03.30
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초록

This article concerns a property of local rings and domains. A ring R is called weakly local if for every a ∈ R, a is regular or 1-a is regular, where a regular element means a non-zero-divisor. We study the structure of weakly local rings in relation to several kinds of factor rings and ring extensions that play roles in ring theory. We prove that the characteristic of a weakly local ring is either zero or a power of a prime number. It is also shown that the weakly local property can go up to polynomial (power series) rings and a kind of Abelian matrix rings.

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참고문헌

  1. E.H. Feller, Properties of primary noncommutative rings, Trans. Amer. Math. Soc. 89 (1958), 79-91. https://doi.org/10.1090/S0002-9947-1958-0098763-0
  2. K.R. Goodearl and R.B. Warfield Jr., An Introduction to Noncommutative Noe- therian Rings, Cambridge University Press, Cambridge-New York-Port Chester- Melbourne-Sydney, 1989.
  3. C.Y. Hong, H.K. Kim, N.K. Kim, T.K. Kwak and Y. Lee, Duo property on the monoid of regular elements, (submitted).
  4. C. Huh, H.K. Kim and Y. Lee, p.p. rings and generalized p.p.. rings, J. Pure Appl. Algebra 167 (2002), 37-52. https://doi.org/10.1016/S0022-4049(01)00149-9
  5. C. Huh, Y. Lee and A. Smoktunowicz, Armendariz rings and semicommutative rings, Comm. Algebra 30 (2002), 751-761. https://doi.org/10.1081/AGB-120013179
  6. S.U. Hwang, N.K. Kim and Y. Lee, On rings whose right annihilators are bounded, Glasgow Math. J. 51 (2009) 539-559. https://doi.org/10.1017/S0017089509005163
  7. N.K. Kim and Y. Lee, Armendariz rings and reduced rings, J. Algebra 223 (2000), 477-488. https://doi.org/10.1006/jabr.1999.8017
  8. J. Lambek, Lectures on Rings and Modules, Blaisdell Publishing Company, Waltham, 1966.
  9. J.C. McConnell and J.C. Robson, Noncommutative Noetherian Rings, John Wiley & Sons Ltd., Chichester, New York, Brisbane, Toronto, Singapore, 1987.