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http://dx.doi.org/10.11568/kjm.2014.22.2.279

REVERSIBILITY OVER PRIME RADICALS  

Jung, Da Woon (Department of Mathematics Pusan National University)
Lee, Yang (Department of Mathematics Education Pusan National University)
Sung, Hyo Jin (Department of Mathematics Education Pusan National University)
Publication Information
Korean Journal of Mathematics / v.22, no.2, 2014 , pp. 279-288 More about this Journal
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 quasi-reversible-over-prime-radical (simply, QRPR) as a generalization of the 2-primal ring property. A ring is called 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.
Keywords
quasi-reversible-over-prime-radical ring (QRPR ring); prime radical; 2-primal ring; semicommutative ring; NI ring; weakly semicommutative ring;
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