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http://dx.doi.org/10.4134/CKMS.c170003

ON COMMUTATIVITY OF NILPOTENT ELEMENTS AT ZERO  

Abdul-Jabbar, Abdullah M. (Department of Mathematics University of Salahaddin-Erbil)
Ahmed, Chenar Abdul Kareem (Department of Mathematics University of Zakho)
Kwak, Tai Keun (Department of Mathematics Daejin University)
Lee, Yang (Institute of Basic Science Daejin University)
Publication Information
Communications of the Korean Mathematical Society / v.32, no.4, 2017 , pp. 811-826 More about this Journal
Abstract
The reversible property of rings was initially introduced by Habeb and plays a role in noncommutative ring theory. In this note we study the reversible ring property on nilpotent elements, introducing the concept of commutativity of nilpotent elements at zero (simply, a CNZ ring) as a generalization of reversible rings. We first find the CNZ property of 2 by 2 full matrix rings over fields, which provides a basis for studying the structure of CNZ rings. We next observe various kinds of CNZ rings including ordinary ring extensions.
Keywords
CNZ ring; reversible ring; matrix ring; polynomial ring; skew Laurent polynomial ring;
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Times Cited By KSCI : 2  (Citation Analysis)
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