Wreath products of acts over monoids: I. regular and inverse acts

AbstractLet R, S be monoids and A, B be left R- and S-acts, respectively, a∈A is called regular (inverse) if there exists a (unique) homomorphism ϕ : Ra → R with ϕ(a)a = a. The wreath product of acts A × B over the wreath product R × F(A, S) of R and S by A is defined where F(A, S) denotes all mappings from A to S. Regular and inverse elements in the wreath product A × B are characterized as well as global regular and inverse wreath products A × B. As one kind of example free S-acts F over F and over EndsF are considered. Relations to (von Neuman) regular and inverse monoids are indicated