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Keywords:
unified product; Schützenberger product; regularity
unified product; Schützenberger product; regularity
Summary:
We first define a new monoid construction (called unified-like product $O\mathbin {\Diamond _{\Omega }}J$) under a unified product $O\bowtie J$ and the Schützenberger product $O\mathbin {\Diamond } J$. 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 $O\mathbin {\Diamond _{\Omega }}J$ to be regular.
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