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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{AL_2022_61_6_a7,
     author = {A. A. Stepanova},
     title = {Generalized stability of the class of injective $S$-acts},
     journal = {Algebra i logika},
     pages = {784--795},
     publisher = {mathdoc},
     volume = {61},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2022_61_6_a7/}
}
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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/