GENERALIZED STABILITY OF THE CLASSOF INJECTIVES S -ACTS

The concept of P-stability is a particular case of generalized stability of complete theories. We study injective S-acts with a P-stable theory. It is proved that the class of injective S-acts is (P, 1)-stable only if S is a one-element monoid. Also we describe commutative and linearly ordered monoids S the class of injective S-acts over which is (P, s)-, (P, a)-, and (P, e)-stable.

Automated summary

The paper focuses on injective S-acts with a P-stable theory and proves that the class of injective S-acts is (P, 1)-stable only if S is a one-element monoid. Additionally, it describes commutative and linearly ordered monoids S for which the class of injective S-acts is (P, s)-, (P, a)-, and (P, e)-stable.