Group inverses of matrices over right Ore domains (Q428114)

An integral domain \(R\) is called a right Ore domain if for any pair of nonzero elements \(x,y \in R\), there exists a pair of elements \(u,v \in R\) such that \(xu=yv=0\). A left Ore domain is defined similarly. A Bezout domain is an integral domain in which every pair of elements has a greatest common divisor that is a linear combination of them. Bezout domains are both left and right Ore domains. In the paper under review, the authors present equivalent conditions for the existence of the group inverses of certain structured block matrices over a right Ore domain and a Bezout domain. Representations for the group inverses are also given.