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Weakly Clean Ideal (1704.08814v1)
Published 28 Apr 2017 in math.RA
Abstract: Motivated by the concept of clean ideals, we introduce the notion of weakly clean ideals. We define an ideal $I$ of a ring $R$ to be weakly clean ideal if for any $x\in I$, $x=u+e$ or $x=u-e$, where $u$ is a unit in $R$ and $e$ is an idempotent in $R$. We discuss various properties of weakly clean ideals.
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