On generalized conditionally commutative semigroups
The graph product is an operator mixing direct and free products. It is already known that free products and direct products of automatic monoids are automatic. The main aim of this paper is to prove that graph products of automatic monoids of finite geometric type are still automatic. A similar result for prefix-automatic monoids is established.
The graph product is an operator mixing direct and free products. It is already known that free products and direct products of automatic monoids are automatic. The main aim of this paper is to prove that graph products of automatic monoids of finite geometric type are still automatic. A similar result for prefix-automatic monoids is established.
In this paper the equivalence on a semigroup in terms of a set of idempotents in is defined. A semigroup is called a -liberal semigroup with as the set of projections and denoted by if every -class in it contains an element in . A class of -liberal semigroups is characterized and some special cases are considered.