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 characterizations of the weighted core inverse of sum and the difference between two weighted core invertible elements in a ring with involution under different conditions. Further, we discuss reverse order and mixed-type reverse order laws for the weighted core invertible elements in a ring.