<abstract xmlns="http://www.w3.org/1999/xhtml"> 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 </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

Quasipolar Subrings of 3 x 3 Matrix Rings

Department of Mathematics, Ankara University, Turkey

Department of Mathematics, Hacettepe University, Turkey

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

{"article-title":"Quasipolar Subrings of 3 x 3 Matrix Rings"}

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 Subrings of 3 x 3 Matrix Rings

Published Online: Mar 05, 2014

Page range: 133 - 146

DOI: https://doi.org/10.2478/auom-2013-0048

Keywords
Quasipolar ring, local ring, 3 x 3 matrix ring

This content is open access.

Quasipolar Subrings of 3 x 3 Matrix Rings

Published Online: Mar 05, 2014

Page range: 133 - 146

DOI: https://doi.org/10.2478/auom-2013-0048

KeywordsQuasipolar ring, local ring, 3 x 3 matrix ring

This content is open access.

Keywords
Quasipolar ring, local ring, 3 x 3 matrix ring