Geodesic
Equations over direct powers of algebraic structures in relational languages
Prikladnaâ diskretnaâ matematika, no. 3 (2021), pp. 5-11.

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For a semigroup $S$ (group $G$) we study relational equations and describe all semigroups $S$ with equationally Noetherian direct powers. It follows that any group $G$ has equationally Noetherian direct powers if we consider $G$ as an algebraic structure of a certain relational language. Further we specify the results as follows: if a direct power of a finite semigroup $S$ is equationally Noetherian, then the minimal ideal $\text{Ker}(S)$ of $S$ is a rectangular band of groups and $\text{Ker}(S)$ coincides with the set of all reducible elements.
Keywords: groups, semigroups, direct powers, equationally Noetherian algebraic structures.
Mots-clés : relations 
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A. Shevlyakov. Equations over direct powers of algebraic structures in relational languages. Prikladnaâ diskretnaâ matematika, no. 3 (2021), pp. 5-11. http://geodesic.mathdoc.fr/item/PDM_2021_3_a0/

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