Weakly I-clean rings
Abstract
In this article, we introduce the concept of weakly I-clean ring, for any ideal I of a ring R. We show that, for an ideal I of a ring R, R is uniquely weakly I-clean if and only if R/I is semi boolean and idempotents can be lifted uniquely weakly modulo I if and only if for each a∈ R, there exists a central idempotent e∈ R such that either a-e∈ I or a+e∈ I and I is idempotent free. As a corollary, we characterize weakly J-clean ring. Also we study various properties of weakly I-clean ring.
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