Wreath product and infinite words (Q1587974)

The wreath product of semigroups is extended to \(\omega\)-semigroups in a natural way so that the ``wreath product principle'' holds in a strong form. This variant of the principle characterizes \(\omega\)-languages recognized by wreath products \(S\circ T\) of \(\omega\)-semigroups in terms of inverse images of \(\omega\)-languages recognized by the first factor \(S\) by sequential functions. The principle is applied to obtain decomposition results for pseudovarieties of \(\omega\)-semigroups associated with a pseudovariety of semigroups.