Main Article Content
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.
Keywords
weakly clean rings
clean rings
nilpotents
Jacobson radical
Article Details
How to Cite
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
