Geodesic
Cantor property of quasi-unitary acts over completely (0-)simple semigroups
Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 1, pp. 27-33

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A universal algebra $A$ is called cantorian if for any algebra $B$ of the same signature, the existence of injective homomorphisms $A\to B$ and $B \to A$ implies an isomorphism of algebras $A$ and $B$. A right act $X$ over a semigroup $S$ is called quasiunitary if $X=XS$. We prove that every quasiunitary act over a completely simple semigroup and also every quasiunitary act with zero over a completely 0-simple semigroup are cantorian. 
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     title = {Cantor property of quasi-unitary acts over completely (0-)simple semigroups},
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I. B. Kozhukhov; A. S. Sotov. Cantor property of quasi-unitary acts over completely (0-)simple semigroups. Dalʹnevostočnyj matematičeskij žurnal, Tome 23 (2023) no. 1, pp. 27-33. http://geodesic.mathdoc.fr/item/DVMG_2023_23_1_a3/