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arXiv · 1211.5286

Strongly Nil-*-Clean Rings

Huanyin Chen·Abdullah Harmanci·A. Cigdem Ozcan
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Abstract

A *-ring $R$ is called a strongly nil-*-clean ring if every element of $R$ is the sum of a projection and a nilpotent element that commute with each other. In this article, we show that $R$ is a strongly nil-*-clean ring if and only if every idempotent in $R$ is a projection, $R$ is periodic, and $R/J(R)$ is Boolean. For any commutative *-ring $R$, we prove that the algebraic extension $R[i]$ where $i^2=μi+η$ for some $μ,η\in R$ is strongly nil-*-clean if and only if $R$ is strongly nil-*-clean and $μη$ is nilpotent. The relationships between Boolean *-rings and strongly nil-*-clean rings are also obtained.

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Huanyin Chen, Abdullah Harmanci, A. Cigdem Ozcan. 2013-09-05. Strongly Nil-*-Clean Rings. https://arxiv.org/abs/1211.5286

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