Generalized stability of the class of injective $S$-acts

A. A. Stepanova

Far Eastern Federal University, Vladivostok

Abstract: 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.

Keywords: monoid, act over monoid, injective act, generalized stability.

UDC: 510.67:512.56

Received: 04.03.2022
Revised: 13.10.2023

DOI: 10.33048/alglog.2022.61.607

 English version: Algebra and Logic, 2022, 61:6, 537–544