2022/04/30 by Huihui Zhu, Zhu, Huihui, Liyun Wu +3
Computer Science · #15A09 #16W10 #FOS: Mathematics #Matrix Theory and Algorithms #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2205.00181
openalex publication_date 2022/04/30 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
Let S be a *-semigroup and let a,w,v∈ S. The initial goal of this work is to introduce two new classes of generalized inverses, called the w-core inverse and the dual v-core inverse in S. An element a∈ S is w-core invertible if there exists some x∈ S such that awx2=x, xawa=a and (awx)^*=awx. Such an x is called a w-core inverse of a. It is shown that the core inverse and the pseudo core inverse can be characterized in terms of the w-core inverse. Several characterizations of the w-core inverse of a are derived, and the expression is given by the inverse of w along a and \1,3\-inverses of a in S. Also, the connections between the w-core inverse and other generalized inverses are given. In particular, when S is a *-ring, the existence criterion for the w-core inverse is given by units. The dual v-core inverse of a is defined by the existence of y∈ S satisfying y2va=y, avay=a and (yva)^*=yva. Dual results for the dual v-core inverse also hold.