We describe monoids S such that the theory of the class of all divisible S-acts is stable, superstable or, for commutative monoid, ω- stable. More precisely, we prove that the theory of the class of all divisible S-acts is stable (superstable) iff S is a linearly ordered (well ordered) monoid. We also prove that for a commutative monoid S the theory of the class of all divisible S-acts is ω-stable iff S is either an abelian group with at most countable number of subgroups or is finite and has only one proper ideal. Classes of regular, projective and strongly flat S-acts were considered in [1, 2]. Using results from [3] we obtain necessary and sufficient conditions for stability, superstability and ω-stability of theories of classes of all divisible S-acts.
展开▼
