Extensions of Rings Having McCoy Condition

Abstract

Let R be an associative ring with unity. Then R is said to be a right McCoy ring when the equation f(x)g(x) = 0 (over R[x]), where 0 not equal f (x), g(x) is an element of R[x],implies that there exists a nonzero element c is an element of R such that f(x)c = 0. In this paper, we characterize some basic ring extensions of right McCoy rings and we prove that if R is a right McCoy ring, then R[x]/(x(n)) is a right McCoy ring for any positive integer n >= 2.