Equations over direct powers of algebraic structures in relational languages | Prikladnaya Diskretnaya Matematika - Applied Discrete Mathematics. 2021. № 53. DOI: 10.17223/20710410/53/1

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.