Commun. Korean Math. Soc.
Published online March 8, 2019
mete burak calci, sait halicioglu, and 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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