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Analele Universitatii "Ovidius" Constanta - Seria Matematica

The Journal of "Ovidius" University of Constanta

Editor-in-Chief: Flaut, Cristina

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Open Access
Online
ISSN
1844-0835
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Quasipolar Subrings of 3 x 3 Matrix Rings

Orhan Gurgun / Sait Halicioglu / Abdullah Harmanci
Published Online: 2014-03-05 | DOI: https://doi.org/10.2478/auom-2013-0048

Abstract

An element a of a ring R is called quasipolar provided that there exists an idempotent p ∈ R such that p ∈ comm2(a), a + p ∈ U (R) and ap ∈ Bqnil. A ring R is quasipolar in case every element in R is quasipolar. In this paper, we determine conditions under which subrings of 3 x 3 matrix rings over local rings are quasipolar. Namely, if R. is a bleached local ring, then we prove that T3 (R) is quasipolar if and only if R is uniquely bleached. Furthermore, it is shown that Tn(R) is quasipolar if and only if Tn(R[[x]]) is quasipolar for any positive integer

Keywords: Quasipolar ring; local ring; 3 x 3 matrix ring

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About the article

Published Online: 2014-03-05

Published in Print: 2013-11-01


Citation Information: Analele Universitatii "Ovidius" Constanta - Seria Matematica, ISSN (Online) 1844-0835, DOI: https://doi.org/10.2478/auom-2013-0048.

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