Equations over direct powers of algebraic structures in relational languages

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DOI Доступ к ресурсу на сайте издателя			10.17223/20710410/53/1

Title: Equations over direct powers of algebraic structures in relational languages
Creator: Shevlyakov, A. N.
Date: 2021
DOI: 10.17223/20710410/53/1
Description: 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 Ker(S) of S is a rectangular band of groups and Ker(S) coincides with the set of all reducible elements.