Geodesic
Uniform $m$-equivalences and numberings of classical systems
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 49-65

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The paper considers the representability of algebraic structures (groups, lattices, semigroups, etc.) over equivalence relations on natural numbers. The concept of a (uniform) $m$-equivalence is studied. It is proved that the numbering equivalence of any numbered group is a uniform $m$-equivalence. On the other hand, we construct an example of a uniform $m$-equivalence over which no group is representable. Additionally we show that there exists a positive equivalence over which no upper (lower) semilattice is representable.
Keywords: uniform $m$-equivalence, lattice, field.
Mots-clés : group 
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     title = {Uniform $m$-equivalences and numberings of classical systems},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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     year = {2022},
     language = {en},
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N. Kh. Kasymov; R. N. Dadazhanov; S. K. Zhavliev. Uniform $m$-equivalences and numberings of classical systems. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 1, pp. 49-65. http://geodesic.mathdoc.fr/item/SEMR_2022_19_1_a2/