Sytongly P-clean Rings and Matrices

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8098.pdf (305.51 KB)

Date

2014

Authors

Chen, H.
Kose, H.
Kurtulmaz, Y.

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Source Title

Journal of Algebra and its Applications

Print ISSN

0024-3795

Electronic ISSN

1873-1856

Publisher

Elsevier

Volume

15

Issue

Pages

116 - 131

Language

English

Type

Article

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Abstract

Abstract. An element of a ring R is strongly P-clean provided that it can be written as the sum of an idempotent and a strongly nilpotent element that commute. A ring R is strongly P-clean in case each of its elements is strongly P-clean. We investigate, in this article, the necessary and sufficient conditions under which a ring R is strongly P-clean. Many characterizations of such rings are obtained. The criteria on strong P-cleanness of 2 × 2 matrices over commutative projective-free rings are also determined.

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Keywords

Strongly P-clean ring, n×n matrix, Projective-free ring, Uniquely nil-clean ring, 16S50, 16U99, Boolean ring

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http://hdl.handle.net/11693/12587

Published Version (Please cite this version)

https://dx.doi.org/10.24330/ieja.266242

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Scholarly Publications - Mathematics