Geodesic
Generalized stability of the class of injective $S$-acts
Algebra i logika, Tome 61 (2022) no. 6, pp. 784-795.

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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. 
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     title = {Generalized stability of the class of injective $S$-acts},
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A. A. Stepanova. Generalized stability of the class of injective $S$-acts. Algebra i logika, Tome 61 (2022) no. 6, pp. 784-795. http://geodesic.mathdoc.fr/item/AL_2022_61_6_a7/

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