\(\mathcal P\)-regular semigroups.
Regular *-semigroups and orthodox semigroups have some common properties regarding the inverses of elements of these semigroups. These properties are in relation to the set of all projections, for regular *-semigroups, and in relation to the set of all idempotents, for orthodox semigroups. Let \(P\) denote the sets just specified, for these classes of semigroups. Then, the following is a key property that holds for both classes: let \(a'\) be an inverse of \(a\) and let \(b'\) be an inverse of \(b\) such that \(aa'\), \(a'a\), \(bb'\), \(b'b\) all belong to \(P\). Then \(b'a'\) is an inverse of \(ab\) and \(abb'a'\) and \(b'a'ab\) both belong to \(P\). This paper studies the properties of a class of semigroups giving a generalization of these shared properties of regular *-semigroups and orthodox semigroups.
scientific article; zbMATH DE number 4085917
scientific article