Conditions for Acts over Semilattices to be Cantor

An algebra is said to be Cantor if a theorem similar to the Cantor– Bernstein– Schröder theorem holds for it; namely, if, for any algebra , the existence of injective homomorphisms and implies the isomorphism . Necessary and sufficient conditions for an act over a finite commutative semigroup of ide...

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Bibliographic Details
Published in:	Mathematical Notes Vol. 109; no. 3-4; pp. 593 - 599
Main Authors:	Kozhukhov, I. B., Sotov, A. S.
Format:	Journal Article
Language:	English
Published:	Moscow Pleiades Publishing 01-03-2021
Subjects:	14/34 639/766/189 639/766/530 639/766/747 Mathematics Mathematics and Statistics act over a semigroup semilattice Cantor–Bernstein–Schröder theorem
Online Access:	Get full text
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Summary:	An algebra is said to be Cantor if a theorem similar to the Cantor– Bernstein– Schröder theorem holds for it; namely, if, for any algebra , the existence of injective homomorphisms and implies the isomorphism . 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.
ISSN:	0001-4346 1573-8876
DOI:	10.1134/S0001434621030287