Further results on weighted core inverse in a ring

Abstract

The notion of the weighted core inverse in a ring with involution was introduced, recently [ Mosić et al. Comm. Algebra, 2018; 46(6); 2332-2345. In this paper, we explore new representation and characterization of the weighted core inverse of sum and difference of two weighted core invertible elements in ring with involution under different conditions. Further, we discuss reverse order laws and mixed-type reverse order laws for the weighted core invertible elements in a ring.