본문 바로가기
KERD
논문KCI 등재

On ø-von Neumann regular rings

Gaohua Tang|Fanggui Wang|Wei Zhao
대한수학회 (The Korean Mathematical Society)|2013.01|대한수학회지 (Journal of the KMS)|제50권 제1호|pp. 219-229

1

조회

0

다운로드

10

인용

0

참고문헌

키워드

ø-torsion modulesø-flat modulesø-von Neumann regular rings
주제분류수학

초록

Let R be a commutative ring with 1≠0 and let H={R|R is a commutative ring and Nil(R) is a divided prime ideal}. If R∈H}, then R is called a ø-ring. In this paper, we introduce the concepts of ø-torsion modules, ø-flat modules, and ø-von Neumann regular rings.

Abstract

Let R be a commutative ring with 1≠0 and let H={R|R is a commutative ring and Nil(R) is a divided prime ideal}. If R∈H}, then R is called a ø-ring. In this paper, we introduce the concepts of ø-torsion modules, ø-flat modules, and ø-von Neumann regular rings.

참고문헌 (20)

  1. D. F. Anderson, "On Φ-Pr¨ufer rings and Φ-Bezout rings", Houston J. Math, 30(2), pp.331~343 (2004)
  2. D. F. Anderson, "onΦ-Dedekind rings and Φ-Krull rings", Houston J. Math, 31(4), pp.1007~1022 (2005)
  3. A. Badawi, "On divided commutative rings", Comm. Algebra, 27(3), pp.1465~1474 (1999)
  4. A. Badawi, "On Φ-pseudo-valuation rings, Advances in commutative ring theory", Lecture Notes in Pure and Appl. Math., 205, pp.101~110 (1999), Dekker
  5. A. Badawi, "On Φ-pseudo-valuation rings. II", Houston J. Math, 26(3), pp.473~480 (2000)
  6. A. Badawi, "OnΦ-chained rings and Φ-pseudo-valuation rings", Houston J. Math, 27(4), pp.725~736 (2001)
  7. A. Badawi, "Φ-pseudo-valuation rings, Commutative rings", pp.5~14 (2002), Nova Sci. Publ.
  8. A. Badawi, "On Nonnil-Noetherian rings", Comm. Algebra, 31(4), pp.1669~1677 (2003)
  9. A. Badawi, "Factoring nonnil ideals as a product of prime and invertible ideals", Bulletin of the London Matth. Society, 37, pp.665~672 (2005)
  10. A. Badawi, "On rings with divided nil ideal: a survey, In Commutative algebra and its appli- cations", pp.21~40 (2009), Walter de Gruyter
  11. A. Badawi, "Strong ring extensions and Φ-pseudo-valuation rings", Hous- ton J. Math, 32(2), pp.379~398 (2006)
  12. A. Badawi, "Some finiteness conditions on the set of overrings of a Φ-ring", Houston J. Math, 34(2), pp.397~408 (2008)
  13. A. Badawi, "Rings with prime nilradical, in Arithmetical Properties of Commutative Rings and Monoids", Lect. Notes Pure Appl. Math., 241, pp.198~212 (2005), Chapman & Hall[DOI]
  14. A. Badawi, "on Φ-Mori rings", Houston J. Math, 32(1), pp.1~32 (2006)
  15. D. E. Dobbs, "Divided rings and going-down", Pacific J. Math, 67(2), pp.353~363 (1976)
  16. S. Hizem, "Nonnil-Noetherian rings and the SFT property", Rocky Moun- tain J. Math, 41(5), pp.1483~1500 (2011)
  17. J. A. Huckaba, "Commutative Rings with Zero Divisors" (1988), Marcel Dekker
  18. H. Kim, "On Φ-strong Mori rings", Houston J. Math, 38(2), pp.359~371 (2012)
  19. C. Lomp, "Comparability, distributivity and non-commutative Φ-rings, Groups, rings and group rings", Contemp. Math., 499, pp.205~217 (2009), Amer. Math. Soc.
  20. F. G. Wang, "Commutative Rings and Star-Operation Theory" (2006), Sicence Press

이 간행물의 다른 논문 (13건)

Representation theorems for multivalued pramartsFettah Akhiat, Fatima Ezzakipp. 1-16Multiple valued iterative dynamics models of nonlinear discrete-time control dynamical systems with disturbanceByungik Kahngpp. 17-39Existence and controllability results for nondensely defined stochastic evolution differential inclusions with nonlocal conditionsJin Bo Ni, Feng Xu, Juan Gaopp. 41-59α-completely positive maps on locally C*-algebras, Krein modules and Radon-Nikodym theorem허재성, 지운식, 김영이pp. 61-80A cell boundary element method for a flux control problem이형천, 전영목pp. 81-93
원문 보기