On Nil-Symmetric Rings

Uday Shankar Chakraborty and Krishnendu Das

Journal of Mathematics, 2014, vol. 2014, 1-7

Abstract:

The concept of nil-symmetric rings has been introduced as a generalization of symmetric rings and a particular case of nil-semicommutative rings. A ring is called right (left) nil-symmetric if, for , where are nilpotent elements, implies . A ring is called nil-symmetric if it is both right and left nil-symmetric. It has been shown that the polynomial ring over a nil-symmetric ring may not be a right or a left nil-symmetric ring. Further, it is also proved that if is right (left) nil-symmetric, then the polynomial ring is a nil-Armendariz ring.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:483784

DOI: 10.1155/2014/483784

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