Monoids with disjunctive identity and their codes (Q1091482)

The authors find several properties of monoids with disjunctive identity (that is, monoids whose only congruence for which 1 is a congruence class is the trivial congruence). Since a disjunctive identity of a finitely generated monoid corresponds to a strong code in the sense of \textit{H. J. Shyr} [see Soochow J. Math. Nat. Sci. 3, 9-16 (1977; Zbl 0388.94016)], the authors find some properties of infinite strong codes and of a special class of such codes. It turns out that these special strong codes are tightly connected with the Dyck languages. They also consider special monoid presentations, thus gaining an additional insight into the structure of these classes of monoids and codes.