On Nil-Symmetric Rings. (16th October 2014) - Chakraborty, Uday Shankar; Das, Krishnendu
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.