π -Clean and strongly π -clean rings

On P -Clean Rings

“…Such that t=tb, an element d∈ W is called idempotent if d 2 = d, and an element t∈ W is referred to as nilpotent if a positive integer m exists such that a m = 0 ". [7] "Obviously, every "clean ring" is a P-clean ring; however, We demonstrate a P-clean ring that is not a clean ring. In this work, we discuss the fundamental properties and applications of the P-clean ring ".…”