Finite semigroups with infinite product and languages of infinite words. (Q934184)

The authors give necessary and sufficient conditions for a finite semigroup (respectively, monoid) to have an infinite product compatible with its multiplication. The authors show, in particular, that the family of finite monoids which can be equipped with a strict infinite product constitutes the variety of all finite monoids whose Green relation \(\mathcal R\) is trivial. They also show that a language of infinite words is regular if and only if it is recognized, in a new form, by a finite monoid with infinite product.