WHEN IS AN ABELIAN WEAKLY CLEAN RING CLEAN?

Peter Danchev


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


Keywords


weakly clean rings; clean rings; nilpotents; Jacobson radical

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p-ISSN:2086-8952e-ISSN:2460-0245