Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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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)
  • Received : 2014.04.01
  • Accepted : 2014.05.20
  • Published : 2014.06.30
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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 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.

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