Wreath product and infinite words

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.