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.

Keywords:

• Weighted core inverse
• weighted dual core inverse
• reverse order law
• additive property

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 16W10
• 15A09

Acknowledgments

The authors would like to thank the referees for their detailed comments and suggestions. Further, the author R. Behera would like to thank Prof. R. N. Mohapatra, Department of Mathematics at the University of Central Florida, USA, for useful discussions and encouragement.

Disclosure statement

No potential conflict of interest was reported by the author(s).