Some Properties of Rings of the Type f(x),g(x)-clean

Abstract

In [1], the authors introduced a property of rings called the f(x),g(x)-clean property. We investigate some new results about this property. In particular, we prove that the ring of matrices over a ring R is f(x),g(x)-clean if the ring R is f(x),g(x)-clean as well. We demonstrate, among many other things, that a ring's f(x),g(x)-cleanness may always be passed to R[[x]], but not always to its polynomial ring R[x].