Reversibility over prime radicals
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Abstract
The studies of reversible and $2$-primal rings have done important roles in noncommutative ring theory. We in this note introduce the concept of {\it quasi-reversible-over-prime-radical} (simply, {\it QRPR}) as a generalization of the $2$-primal ring property. A ring is called {\it QRPR} if $ab=0$ for $a, b\in R$ implies that $ab$ is contained in the prime radical. In this note we study the structure of QRPR rings and examine the QRPR property of several kinds of ring extensions which have roles in noncommutative ring theory.
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References
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