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On commutativity of nilpotent elements at zero

곽태근|Abdullah M. Abdul-Jabbar|Chenar Abdul Kareem Ahmed|Yang Lee
대한수학회 (The Korean Mathematical Society)|2017.10|대한수학회논문집 (Communications of the KMS)|제32권 제4호|pp. 811-826

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참고문헌

키워드

matrix ringreversible ringpolynomial ringCNZ ringskew Laurent polynomial ring
주제분류수학

초록

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.

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.

참고문헌 (29)

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