Some new characterizations of core-EP inverse

In this article, several new characterizations of core-EP inverse of an element from an involutory associative ring are given. The core-EP inverse is identified as a particular (b, c)-inverse and an expression for the same is obtained. Further, it is established that an element having core-EP inverse is a strongly π-regular element and the core-EP inverse of an element is a strongly regular element. Motivated by the characterizations of generalized inverses and outer inverses using inverse complements given in the literature, a characterization of core-EP inverse of unit regular elements in a ring with unity is provided using inverse complements and minus partial order.