On condition (G-PWP) (Q2834681)

Let \(S\) be a monoid and \(A\) a right \(S\)-act. Then, \(A\) is said to satisfy the condition (G-PWP), if for all \(a,a'\in A\) and \(s\in S\) such that \(as=a's\) there are \(a''\in A\), \(u,v\in S\) and \(n\in\mathbb N\) such that \(a=a''u\), \(a'=a''v\) and \(us^n=vs^n\). This is a generalization of the condition (PWP) introduced by \textit{V. Laan} [Commun. Algebra 29, No. 2, 829--850 (2001; Zbl 0987.20047)].NEWLINENEWLINEThe authors give several characterizations of monoids \(S\) in terms of right \(S\)-acts satisfying (G-PWP). In particular, they study monoids whose diagonal right act satisfies (G-PWP).