The (j,m)-core inverse in rings with involution

Abstract

Let R be a unital ring with involution. The (j,m)-core inverse of a complex matrixwas extended to an element in R. New necessary and sufficient conditions such that an element in R to be (j,m)-core invertible are given. Moreover, several additive and product properties of two (j,m)-core invertible elements are investigated and a order related to the (j,m)-core inverse is introduced.