Affiliation:
1. School of Mathematics, Hefei University of Technology, Hefei, China
Abstract
Let R be a unital *-ring. This paper establishes necessary and sufficient
conditions for the existence of the w-core inverse of a regular element by
units in R. Then, the existence criterion of the w-core inverse of the
product of three elements are derived. As applications, the existence
criterion and expression of the w-core inverse of 2 ? 2 matrices over a ring
are given.
Publisher
National Library of Serbia
Reference35 articles.
1. O.M. Baksalary, G. Trenkler, Core inverse of matrices, Linear Multilinear Algebra 58 (2010) 681-697.
2. A. Ben-Israel, T.N.E. Greville, Generalized Inverses : Theory and Applications, (2nd edition), Springer, New York 2003.
3. J. Benítez, E. Boasso, The inverse along an element in rings, Electron. J. Linear Algebra 31 (2016) 572-592.
4. J. Benítez, E. Boasso, The inverse along an element in rings with an involution, Banach algebras andC∗-algebras, Linear Multilinear Algebra 65 (2017) 284-299.
5. N. Castro-González, J.L. Chen, L. Wang, Further results on generalized inverses in rings with involution, Electron. J. Linear Algebra 30 (2015) 118-134.