G(X)-QUASI INVO-CLEAN RINGS

Abstract

Let C(R) be the center of a ring R and g(x) 2 C(R)[x] be a xed polynomial. In this paper, we introduce the notion of g(x)-quasi invo-clean rings where every element r can be written as r = v + s, where v 2 Qinv(R) and s is a root of g(x). We study various properties of g(x)-quasi invo-clean rings. We prove that, for an even polynomial g(x), the ring R = Π i2I Ri is g(x)-quasi invo-clean if and only if every Ri is g(x)-quasi invo-clean.