Commun. Korean Math. Soc. 2019; 34(4): 1069-1078
Online first article August 27, 2019 Printed October 31, 2019
https://doi.org/10.4134/CKMS.c180361
Copyright © The Korean Mathematical Society.
Mete B. Calci, Sait Halicioglu, Abdullah Harmanci
, Ankara University; Hacettepe University
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
Supported by: The first author thanks the Scientific and Technological Research Council of Turkey (TUBITAK) for the financial support.
2005; 20(3): 457-466
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd