Czechoslovak Mathematical Journal, Vol. 74, No. 4, pp. 1113-1125, 2024
Unified-like product of monoids and its regularity property
Esra Kirmizi Çetinalp
Received February 29, 2024. Published online October 15, 2024.
Abstract: We first define a new monoid construction (called unified-like product $O {\Diamond_{\Omega}J$) under a unified product $O\bowtie J$ and the Schützenberger product $O \Diamond J$. We investigate whether this algebraic construction defined with operations of the unified and Schützenberger product specifies a monoid or not. Then, we obtain a presentation of this new product for any two monoids. Finally, we define the necessary and sufficient conditions for $O \Diamond_{\Omega}J$ to be regular.