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On Semicommutative Modules and Rings

Abdullah Harmanci|Nazim Agayev
경북대학교 자연과학대학 수학과|2007.03|Kyungpook Mathematical Journal|제47권 제1호|pp. 21-30

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Abstract

We say a module M R a semicommutative moduleif for anym 2 M and anya 2 R, ma = 0 implies mRa = 0. This paper gives various properties of reduced, Ar-mendariz, Baer, Quasi-Baer,p:p:and p:q:-Baer rings to extend to modules. In additionwe also prove, for a p.p.-ringR,R is semicommutative iR is Armendariz. LetR be anabelian ring and M R be a p:p:-module, thenM R is a semicommutative module iM R isan Armendariz module. For any ring R,R is semicommutative iA(R;) is semicommu-tative. LetR be a reduced ring, it is shown that for numbern 4 and k = [n=2];Tkn (R)is semicommutative ring butTk 1n (R) is not.

참고문헌 (11)

  1. "On Reduced^Semicommutative Modules", 30, pp.285~291 (2006)
  2. "Principally Quasi-Baer Rings", 29, pp.639~660 (2001)
  3. "Semicommutative Modules Armendariz Modules", 8, pp.53~65
  4. "Armendariz Rings Semicommutative Rings", 30, pp.751~761 (2002)
  5. "Bijective Extension of Injective Ring Endomorphisms", pp.435~448 (1982)
  6. "Armendariz Rings^Reduced Rings", 223, pp.477~488 (2000)
  7. "New York"
  8. "Reduced Modules, Rings, modules, algebras and abelian groups", 236, pp.365~377 (2004), Dekker, New york
  9. "Armendariz Reduced Rings", 32(6), pp.2287~2299 (2004)
  10. "Armendariz rings", 73(A), pp.14~17 (1997)
  11. "Baer and Quasi-Baer Modules", 32, pp.103~123 (2004)

관련 논문AI추천

A Note on Semi-Projective ModulesH. Tansee, S. Wongwal경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2002 · 제42권 제2호On a Class of Semicommutative RingsAbdullah Harmanci, Nazim Agayev, Tahire Özen경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2011 · 제51권 제3호Semi-Primeness of the Endomorphism Ring of a Projective ModuleSoon-Sook Bae대한수학회 · 대한수학회논문집2003 · 제18권 제4호A Note on -Separative ModulesHuanyin Chen경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2007 · 제47권 제3호On rings containing a p-injective maximal left idealJin Yong Kim, Nam Kyun Kim대한수학회 · 대한수학회논문집2003 · 제18권 제4호A Commutativity Theorem for RingsM.S.S.Khan경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2003 · 제43권 제4호

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