Geodesic
Unified-like product of monoids and its regularity property
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1113-1125 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.21136/CMJ.2024.0081-24
Classification : 16S15, 20D40, 20L05
Keywords: unified product; Schützenberger product; regularity 
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     title = {Unified-like product of monoids and its regularity property},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1113--1125},
     year = {2024},
     volume = {74},
     number = {4},
     doi = {10.21136/CMJ.2024.0081-24},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2024.0081-24/}
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Kırmızı Çetinalp, Esra. Unified-like product of monoids and its regularity property. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1113-1125. doi: 10.21136/CMJ.2024.0081-24

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