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http://dx.doi.org/10.4134/JKMS.j180364

REVERSIBILITY AND SYMMETRY OVER CENTERS  

Choi, Kwang-Jin (Smith Liberal Arts College Sahmyook University)
Kwak, Tai Keun (Department of Mathematics Daejin University)
Lee, Yang (Department of Mathematics Yanbian University)
Publication Information
Journal of the Korean Mathematical Society / v.56, no.3, 2019 , pp. 723-738 More about this Journal
Abstract
A property of reduced rings is proved in relation with centers, and our argument in this article 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 given reversible-over-center rings, 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;
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Times Cited By KSCI : 2  (Citation Analysis)
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