Equations over direct powers of algebraic structures in relational languages A. N. Shevlyakov
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ArticleContent type: Текст Media type: электронный Subject(s): группы | полугруппы | алгебраические структуры | реляционные языкиGenre/Form: статьи в журналах Online resources: Click here to access online
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Прикладная дискретная математика № 53. С. 5-11Abstract: 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.
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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 Ker(S) of S is a rectangular band of groups and Ker(S) coincides with the set of all reducible elements.
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