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This article is cited in 1 scientific paper (total in 1 paper)
Conditions for Acts over Semilattices to be Cantor
I. B. Kozhukhovab, A. S. Sotovb a National Research University of Electronic Technology
b Moscow Center for Fundamental and Applied Mathematics
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.
Keywords:
act over a semigroup, semilattice, Cantor–Bernstein–Schröder theorem.
Received: 26.02.2020 Revised: 16.01.2021
Citation:
I. B. Kozhukhov, A. S. Sotov, “Conditions for Acts over Semilattices to be Cantor”, Mat. Zametki, 109:4 (2021), 581–589; Math. Notes, 109:4 (2021), 593–599
Linking options:
https://www.mathnet.ru/eng/mzm12703https://doi.org/10.4213/mzm12703 https://www.mathnet.ru/eng/mzm/v109/i4/p581
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Abstract page: | 172 | Full-text PDF : | 50 | References: | 17 | First page: | 19 |
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