FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Cantor property of quasi-unitary acts over completely (0-)simple semigroups |
Kozhuhov I. B., Sotov A. S. |
2023, issue 1, P. 27-33 DOI: https://doi.org/10.47910/FEMJ202304 |
Abstract |
| An 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. |
Keywords: act over semigroup, universal algebra, finiteness condition. |
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References |
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