Geodesic
Conditions for Acts over Semilattices to be Cantor
Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 581-589

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An algebra $A$ is said to be Cantor if a theorem similar to the Cantor–Bernstein–Schröder theorem holds for it; namely, if, for any algebra $B$, the existence of injective homomorphisms $A\to B$ and $B\to A$ implies the isomorphism $A\cong B$. Necessary and sufficient conditions for an act over a finite commutative semigroup of idempotents to be Cantor are obtained under the assumption that all connected components of this act are finite.
Keywords: act over a semigroup, semilattice, Cantor–Bernstein–Schröder theorem. 
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     author = {I. B. Kozhukhov and A. S. Sotov},
     title = {Conditions for {Acts} over {Semilattices} to be {Cantor}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2021},
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     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a8/}
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I. B. Kozhukhov; A. S. Sotov. Conditions for Acts over Semilattices to be Cantor. Matematičeskie zametki, Tome 109 (2021) no. 4, pp. 581-589. http://geodesic.mathdoc.fr/item/MZM_2021_109_4_a8/