Amalgamated rings with semi nil-clean properties

Abstract

An element in a ring R is said to be semi nil-clean if it is a sum of nilpotent and periodic elements in R. An element in a ring R is said to be semiclean if it is a sum of unit and periodic elements in R. A ring R is said to be semi nil-clean (resp., semiclean) if every element in R is semi nil-clean (resp., semiclean). We discuss some basic properties of semi nil-clean ring and we also study the concepts of semi nil-clean and semiclean properties in various context of commutative rings such as amalgamations and the ring of polynomials R[x] of a ring R.