| In the case where the semigroup variety has a particular closure property with respect to programs, we are able to give precise characterizations of these regular languages. |
| The elements of the semigroup are identified with the reduced words of the rewriting system. |
| It is written for the mathematician who has a background in semigroup theory but knows next to nothing on automata and languages. |
| In this paper we are going to follow their footsteps constructing the skew semigroup ring and prove its associativity without using approximate identity. |
| It follows naturally that various classes of ordered sets can be characterized by semigroup properties of endomorphism semigroups. |
| Equivalently a regular semigroup in which idempotents commute. |
