WHEN IS AN ABELIAN WEAKLY CLEAN RING CLEAN?

Peter Danchev

doi:10.22342/jims.21.2.229.83-91

Peter Danchev ⁽¹⁾

(1) , Bulgaria

https://doi.org/10.22342/jims.21.2.229.83-91

Issue
Volume 21 Number 2 (October 2015)

Submitted
November 3, 2015

Accepted
November 3, 2015

Published
November 3, 2015

Keywords:

weakly clean rings, clean rings, nilpotents, Jacobson radical

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Abstract

We answer the title question in the armative by showing that any
abelian weakly clean ring for which 2 belongs to its Jacobson radical (in particular, if 2 is nilpotent) has to be clean. Some constructive examples, one of which illustrates that this is no longer true removing the condition on the 2, are given as well.

DOI : http://dx.doi.org/10.22342/jims.21.2.229.83-91

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Authors

Peter Danchev

pvdanchev@yahoo.com (Primary Contact)

Author Biography

Peter Danchev

Department of Mathematics, Plovdiv State University
P. Hilendarski", Plovdiv 4000, Bulgaria

Danchev, P. (2015). WHEN IS AN ABELIAN WEAKLY CLEAN RING CLEAN?. Journal of the Indonesian Mathematical Society, 21(2), 83–91. https://doi.org/10.22342/jims.21.2.229.83-91