Reversibility and symmetry over centers
J. Korean Math. Soc.
Published online 2019 Feb 12
Kwang-Jin Choi, Tai Keun Kwak, and Yang Lee
Daejin University, Sahmyook University
Abstract : In this article, a property of reduced rings is proved in relation with centers, and our argument is spread out based on this. It is also proved that the Wedderburn radical coincides with the set of all nilpotents in symmetric-over-center rings, implying that the Jacobson radical, all nilradicals, and the set of all nilpotents are equal in polynomial rings over symmetric-over-center rings. It is shown that reduced rings are reversible-over-center, and that various sorts of reversible-over-center rings can be constructed. The structure of radicals in reversible-over-center and symmetric-over-center rings is also investigated.
Keywords : reversible-over-center ring, reduced ring, symmetric-over-center ring, center, radical, semiprime ring, nilpotent, polynomial ring, matrix ring
MSC numbers : 16U70, 16U80
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