Invo-clean rings associated with central polynomials

Abstract

Let R be an associative ring with identity and let C(R) be the center of a ring R and let g(x) be a fixed polynomial in C(R)[x].  We defined R to be g(x)-invo clean if every element in R can be written as a sum of an involution and a root of g(x).  In this paper, we investigate conditions on a ring to be g(x)-invo clean ring.  Some properties and several examples are given.