Finite images and elementary equivalence of completely regular inverse semigroups
The author extends his result [Proc. Am. Math. Soc. 103, 1041-1048 (1988; Zbl 0642.20001)] and shows that if two diagrams of groups \(G\), \(H\) are finite unions of finitely generated abelian-by-finite groups, then \(G\) and \(H\) are elementarily equivalent iff they have the same finite images. Using an interpretation of completely regular inverse semigroups in terms of diagrams of groups, he proves the analogous theorem about completely regular inverse semigroups which are disjoint unions of finitely generated abelian-by-finite groups. Finally, the author considers diagrams of groups which consist of one group and one or several endomorphisms of this group. In particular, he investigates modules over not necessarily commutative rings.
scientific article; zbMATH DE number 126124
scientific article