Some remarks on the Schützenberger product of n monoids

In Straubing (Theor. Comput. Sci. 13:137–150, 1981), Straubing introduced an n-ary the Schützenberger product on finite monoids. In this paper, we examine this generalization from another point of view and obtain an alternative n-generalized monoid construction of Schützenberger product to facilitate the intelligibility of Straubing’s structure. Then, we find a generator and relator set for this product. Additionally, we compute a complete rewriting system and thus we obtain normal form structure of elements of this monoid construction which could be useful for Automata Theory. This gives us the solvability of the word problem for this product. © 2022, Università degli Studi di Napoli "Federico II".