Geodesic
On additive semigroups of idempotent semirings with identity
Matematičeskie zametki, Tome 116 (2024) no. 4, pp. 552-558

Voir la notice de l'article provenant de la source Math-Net.Ru

The notion of an admissible semigroup is introduced. This is an (additive) semigroup on which a multiplication turning it into a multiplicatively idempotent semiring with identity can be defined. Admissible semilattices are studied. In particular, countable admissible and inadmissible “universal” semilattices are constructed, into which all finite semilattices are isomorphically embedded.
Keywords: semilattice, idempotent semiring, admissible semilattice. 
A. A. Petrov; A. P. Shklyaev. On additive semigroups of idempotent semirings with identity. Matematičeskie zametki, Tome 116 (2024) no. 4, pp. 552-558. http://geodesic.mathdoc.fr/item/MZM_2024_116_4_a4/
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[1] G. Grettser, Obschaya teoriya reshetok, Mir, M., 1982 | MR

[2] L. A. Skornyakov, Elementy teorii struktur, Nauka, M., 1982 | MR

[3] K. Kuratovskii, A. Mostovskii, Teoriya mnozhestv, Mir, M., 1970 | MR

[4] E. M. Vechtomov, A. A. Petrov, Funktsionalnaya algebra i polukoltsa. Polukoltsa s idempotentnym umnozheniem, Lan, Sankt-Peterburg, 2022