On commutativity of nilpotent elements at zero
Commun. Korean Math. Soc. 2017 Vol. 32, No. 4, 811-826
Published online October 31, 2017
Abdullah M. Abdul-Jabbar, Chenar Abdul Kareem Ahmed, Tai Keun Kwak, Yang Lee
Kurdistan Region, Kurdistan Region, Daejin University, Daejin University
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 {\it commutativity of nilpotent elements at zero} (simply, a {\it 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
MSC numbers : 16U80, 16N40
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