Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Semicommutative Modules and Rings

  • Agayev, Nazim (Abant Izzet Baysal University, Faculty of Science and Letters, Department of Mathematics) ;
  • Harmanci, Abdullah (Hacettepe University, Department of Mathematics, Golkoy Campus)
  • Received : 2005.09.16
  • Published : 2007.03.23
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Abstract

We say a module $M_R$ a semicommutative module if for any $m{\in}M$ and any $a{\in}R$, $ma=0$ implies $mRa=0$. This paper gives various properties of reduced, Armendariz, Baer, Quasi-Baer, p.p. and p.q.-Baer rings to extend to modules. In addition we also prove, for a p.p.-ring R, R is semicommutative iff R is Armendariz. Let R be an abelian ring and $M_R$ be a p.p.-module, then $M_R$ is a semicommutative module iff $M_R$ is an Armendariz module. For any ring R, R is semicommutative iff A(R, ${\alpha}$) is semicommutative. Let R be a reduced ring, it is shown that for number $n{\geq}4$ and $k=[n=2]$, $T^k_n(R)$ is semicommutative ring but $T^{k-1}_n(R)$ is not.

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References

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