A Survey of Clean Elements in a Ring: Recent Advances

An element in a ring is called clean if it can be expressed as the sum of an idempotent element and a unit element of the ring. It is called strongly clean if it can be expressed as the sum of an idempotent element and a unit element of the ring which commute. It is called uniquely clean if there is only one way of representing it as the sum of an idempotent and a unit element in the ring. This paper contains an account of recently obtained results on clean, strongly clean and uniquely clean elements in a ring.