Abstract
Let [Formula: see text] be a semiring. An element [Formula: see text] is said to be [Formula: see text]-regular element if there exist [Formula: see text] such that [Formula: see text]. An element [Formula: see text] is called [Formula: see text]-regular clean if [Formula: see text], where [Formula: see text] is an idempotent and [Formula: see text] is a [Formula: see text]-regular element of [Formula: see text]. A semiring [Formula: see text] is said to be a [Formula: see text]-regular clean semiring if every element can be written as the sum of an idempotent and a [Formula: see text]-regular element of [Formula: see text]. In this paper, we introduce the concept of [Formula: see text]-regular clean semiring which generalizes the notion of clean ring, clean semiring and [Formula: see text]-unit clean semiring. We obtain some important characterizations of [Formula: see text]-regular clean semiring in connection with antisimple semiring, inverse semiring and zeroic semiring.