Green's Quasiorder on Menger Algebras of Terms

K. Denecke, P. Glubudom

Abstract

Two elements a, b of a monoid M are related with respect to Green's relation L if there are elements $c, d \in M$ such that a = cb and b = da. The first equation a = cb defines Green's quasiorder $\leq _L$ on M. This quasiorder and Green's relations can also be defined for Menger algebras. After this definition we formulate some elementary propositions for Green's quasiorder $\leq _L$ and then we consider $\leq _L$ in several concrete Menger algebras: n-ary operations, terms and treelanguages. In any case we give a characterization of L and of $\leq _L$.