n-Generalized Schützenberger-Crossed Product of Monoids

We study the n-generalized Schützenberger-crossed product from the viewpoint of combinatorial group theory and introduce a new version of this product. For given monoids of this new product, we obtain a representation of the n-generalized Schützenberger-crossed product of arbitrary monoids. In addition, we give necessary and sufficient conditions for the regularity of this product.