Geodesic
Axiomatizability of the class of subdirectly irreducible $S$-acts over a commutative monoid
Algebra i logika, Tome 62 (2023) no. 2, pp. 266-296.

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An axiomatizability criterion is found for the class of subdirectly irreducible $S$-acts over a commutative monoid. As a corollary, a number of properties are presented which a commutative monoid should satisfy provided that the class of subdirectly irreducible acts over it is axiomatizable. The question about a complete description of monoids over which the class of subdirectly irreducible acts is axiomatizable remains open even for the case of a commutative monoid.
Keywords: $S$-act, commutative monoid, subdirectly irreducible $S$-act, axiomatizable class. 
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A. A. Stepanova; E. L. Efremov. Axiomatizability of the class of subdirectly irreducible $S$-acts over a commutative monoid. Algebra i logika, Tome 62 (2023) no. 2, pp. 266-296. http://geodesic.mathdoc.fr/item/AL_2023_62_2_a5/

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