Regularity of n-generalized Schützenberger product of monoids

Year 2022, Volume: 24 Issue: 1, 71 - 78, 05.01.2022

Esra Kırmızı Çetinalp

https://doi.org/10.25092/baunfbed.903026

Cited By: 1

Abstract

In this work, regularity of $n$-generalized Schützenberger product of monoids from the point of Group Theory is studied. Here, it is determined necessary and sufficient conditions of the $n$-generalized Schützenberger product $A_{1}\Diamond A_{2}\Diamond \cdots \Diamond A_{n}$ to be regular while all $A_{i}\text{ }\left( 1\leqslant i\leqslant n\right)$ are monoids. Also, by considering all $A_{i}\text{ }\left( 1\leqslant i\leqslant n\right)$ to be groups, it is given another result for the regularity of this product.

Keywords

Schützenberger product, monoid, regularity

Monoidlerin n-genelleştirilmiş Schützenberger çarpımının regülerliği

Abstract

Bu çalışmada, monoidlerin $n$-genelleştirilmiş Schützenberger çarpımın regülerliği Grup Teori açısından incelenmiştir. Burada, bütün $A_{i}\text{ }\left( 1\leqslant i\leqslant n\right)$’ler monoid iken $A_{1}\Diamond A_{2}\Diamond \cdots \Diamond A_{n}$ $n$-genelleştirilmiş Schützenberger çarpımın regüler olabilmesi için gerekli ve yeterli koşul elde edilmiştir. Ayrıca, bütün $A_{i}\text{ }\left( 1\leqslant i\leqslant n\right)$’leri grup düşünerek bu çarpımın regülerliği için bir diğer sonuç verilmiştir.

Keywords

Schützenberger çarpım, monoid, regülerlik.

References

• Çetinalp, E.K., Karpuz, E.G. ve Çevik, A.S., Complete rewriting system for Schützenberger product of groups, Asian-European Journal of Mathematics, 12 (1), (2019).
• Çetinalp, E.K. ve Karpuz, E.G., -Generalized Schützenberger Product of Monoids and Complete Rewriting System, Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie, submitted.
• Emin, A., Ateş, F., İkikardeş, S. ve Cangül, İ.N., A new monoid construction under crossed products, J. Inequal. Appl., 244 (2013).
• Gomes, G.M.S., Sezinando, H. ve Pin, J.E., Presentations of the Schützenberger product of groups, Communications in Algebra, 34 (4), 1213-1235, (2006).
• Howie, J.M. ve Ruskuc, N., Constructions and presentations for monoids, Comm. in Algebra, 22 (15), 6209-6224, (1994).
• Karpuz, E.G., Ateş, F. ve Çevik, A.S., Regular and -inverse monoids under Schützenberger products, Algebras, Groups and Geometries, 27, 455-471, (2010).
• Nico, W.R., On the regularity of semidirect products, Journal of Algebra, 80, 29-36, (1983).
• Schützenberger, M.P., On finite monoids having only trivial subgroups, Information and Control, 8, 190-194, (1965).
• Skornjakov, L.A., Regularity of the wreath product of monoids, Semigroup Forum, 18, 83-86, (1979).
• Straubing, H., A generalization of the Schützenberger product of finite monoids, Theo. Comp. Sci., 13, 137-150, (1981).