Very cleanness of generalized matrices

Date
2016-01
Authors
Kurtulmaz, Y.
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Source Title
Bulletin of the Iranian Mathematical Society
Print ISSN
1018-6301
Electronic ISSN
1735-8515
Publisher
Springer
Volume
43
Issue
5
Pages
1457 - 1465
Language
English
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Abstract

An element a in a ring R is very clean in case there exists an idempotent e 2 R such that ae = ea and either a 􀀀 e or a + e is invertible. An element a in a ring R is very J-clean provided that there exists an idempotent e 2 R such that ae = ea and either a􀀀e 2 J(R) or a + e 2 J(R). Let R be a local ring, and let s 2 C(R). We prove that A 2 Ks(R) is very clean if and only if A 2 U(Ks(R)); I A 2 U(Ks(R)) or A 2 Ks(R) is very J-clean.

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