**Authors**

Department of Mathematics, Shahed University, Tehran, Iran

**Abstract**

In this paper, we introduce the new notion of strongly J-clean rings associated with polynomial identity g(x) = 0, as a generalization of strongly J-clean rings. We denote strongly J-clean rings associated with polynomial identity g(x) = 0 by strongly g(x)-J-clean rings. Next, we investigate some properties of strongly g(x)-J-clean.

**Keywords**

- strongly g(x)-clean rings
- strongly g(x)-J-clean rings
- strongly J-clean rings
- rings generated by units

**Main Subjects**