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Journal of Mathematics
Volume 2014, Article ID 483784, 7 pages
http://dx.doi.org/10.1155/2014/483784
Research Article

On Nil-Symmetric Rings

1Department of Mathematics, Albert Einstein School of Physical Sciences, Assam University, Silchar, Assam 788011, India
2Department of Mathematics, Netaji Subhas Mahavidyalaya, Udaipur, Tripura 799120, India

Received 4 May 2014; Accepted 17 September 2014; Published 16 October 2014

Academic Editor: Li Guo

Copyright © 2014 Uday Shankar Chakraborty and Krishnendu Das. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.