Unified-like product of monoids and its regularity property
We first define a new monoid construction (called unified-like product ) under a unified product and the Schützenberger product . 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 to be regular.