On a generalization of principal weak flatness property.
The authors generalize principal weak flatness of acts to GP-flatness. A right \(S\)-act \(A\) is called GP-flat, if for every \(s\in S\), \(S\) a monoid, and any \(a,a'\in A\), \(a\otimes s=a'\otimes s\) in \(A\otimes S\) implies the existence of \(n\in\mathbb N\) such that \(a\otimes s^n=a'\otimes s^n\) in \(A\otimes Ss^n\). They show that GP-flat does not imply weakly flat. The concept is used to characterize so-called generally regular monoids, i.e. monoids \(S\) such that for every \(s\in S\) there exists \(n\in\mathbb N\) and \(x\in S\) such that \(s^n=sxs^n\).
scientific article; zbMATH DE number 6103696