On Nil-Symmetric Rings. (16th October 2014)

• Record Type: Journal Article
• Authors: Chakraborty, Uday Shankar; Das, Krishnendu
• Other Names: Guo Li Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2014(2014)
• Publication Date: 2014-10-16
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2014/483784
• Languages: English
• ISSNs: 2314-4629

Abstract

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 R is called right (left) nil-symmetric if, for a, b, c ∈ R, where a, b are nilpotent elements, a b c = 0 ( c a b = 0 ) implies a c b = 0 . 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 R is right (left) nil-symmetric, then the polynomial ring R [ x ] is a nil-Armendariz ring.