Abstract
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.
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Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 581-589 https://doi.org/10.4213/mzm12703.
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Kozhukhov, I.B., Sotov, A.S. Conditions for Acts over Semilattices to be Cantor. Math Notes 109, 593–599 (2021). https://doi.org/10.1134/S0001434621030287
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DOI: https://doi.org/10.1134/S0001434621030287