Strong $P$-cleanness of trivial Morita contexts
Commun. Korean Math. Soc. 2019 Vol. 34, No. 4, 1069-1078
https://doi.org/10.4134/CKMS.c180361
Published online October 31, 2019
Mete B. Calci, Sait Halicioglu, Abdullah Harmanci
, Ankara University; Hacettepe University
Abstract : Let $R$ be a ring with identity and $P(R)$ denote the prime radical of $R$. An element $r$ of a ring $R$ is called strongly $P$-clean, if there exists an idempotent $e$ such that $r-e=p \in P(R)$ with $ep=pe$. In this paper, we determine necessary and sufficient conditions for an element of a trivial Morita context to be strongly $P$-clean.
Keywords : Morita context, prime radical, strongly $P$-clean ring, strongly clean ring, triangular matrix ring
MSC numbers : 13C99, 16D80, 16U80
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