Abstract
Standard results on the connection between sequential functions and wreath product of semigroups are generalized to infinite words. The definition of wreath product is first extended to ω-semigroups, the proper algebraic framework to study infinite words. The definition is used to extend the wreath product principle, which, in essence, gives a combinatorial description of languages recognized by a wreath product. Finally, these properties lead to new decomposition results for varieties of ω-semigroups.
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