Let f : A → B be a ring homomorphism and K be an ideal of B. Many variations of the notions of clean and nil-clean rings have been studied by a variety of authors. We investigate strongly π-regular and clean-like properties of the amalgamation ring A ◃▹ f K of A with B along K with respect to f .

An element of a ring is clean if it is the sum of an idempotent and a unit. A ring is called clean if each of its elements is clean. In this paper we define a ring is-Clean if each of its elements is the sum of a-regular and an idempotent element. Finally we investigate some properties of-clean rings.