IJPAM: Volume 99, No. 3 (2015)

A GENERALIZATION OF BAER RINGS

K. Paykan$^1$, A. Moussavi$^2$
$^1$Department of Mathematics
Garmsar Branch
Islamic Azad University
Garmsar, IRAN
$^2$Department of Pure Mathematics
Faculty of Mathematical Sciences
Tarbiat Modares University
P.O. Box 14115-134, Tehran, IRAN


Abstract. A ring $R$ is called generalized right Baer if for any non-empty subset $S$ of $R$, the right annihilator $r_R(S^n)$ is generated by an idempotent for some positive integer $n$. Generalized Baer rings are special cases of generalized PP rings and a generalization of Baer rings. In this paper, many properties of these rings are studied and some characterizations of von Neumann regular rings and PP rings are extended. The behavior of the generalized right Baer condition is investigated with respect to various constructions and extensions and it is used to generalize many results on Baer rings and generalized right PP-rings. Some families of generalized right Baer-rings are presented and connections to related classes of rings are investigated.

Received: September 21, 2014

AMS Subject Classification: 16S60, 16D70, 16S50, 16D20, 16L30

Key Words and Phrases: generalized p.q.-Baer ring, generalized PP-ring, PP-ring, quasi Baer ring, Baer ring, Armendariz ring, annihilator

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DOI: 10.12732/ijpam.v99i3.3 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 99
Issue: 3
Pages: 257 - 275


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