Araştırma Makalesi
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Regularity of n-generalized Schützenberger product of monoids

Yıl 2022, , 71 - 78, 05.01.2022
https://doi.org/10.25092/baunfbed.903026

Öz

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.

Kaynakça

  • 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).

Monoidlerin n-genelleştirilmiş Schützenberger çarpımının regülerliği

Yıl 2022, , 71 - 78, 05.01.2022
https://doi.org/10.25092/baunfbed.903026

Öz

Bu çalışmada, monoidlerin nn-genelleştirilmiş Schützenberger çarpımın regülerliği Grup Teori açısından incelenmiştir. Burada, bütün $A_{i}\text{ }\left( 1\leqslant i\leqslant n\right)$’ler monoid iken $A_{1}\Diamond A_{2}\Diamond \cdots \Diamond A_{n}$ nn-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.

Kaynakça

  • 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).
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Araştırma Makalesi
Yazarlar

Esra Kırmızı Çetinalp 0000-0002-8385-7434

Yayımlanma Tarihi 5 Ocak 2022
Gönderilme Tarihi 25 Mart 2021
Yayımlandığı Sayı Yıl 2022

Kaynak Göster

APA Kırmızı Çetinalp, E. (2022). Regularity of n-generalized Schützenberger product of monoids. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 24(1), 71-78. https://doi.org/10.25092/baunfbed.903026
AMA Kırmızı Çetinalp E. Regularity of n-generalized Schützenberger product of monoids. BAUN Fen. Bil. Enst. Dergisi. Ocak 2022;24(1):71-78. doi:10.25092/baunfbed.903026
Chicago Kırmızı Çetinalp, Esra. “Regularity of N-Generalized Schützenberger Product of Monoids”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24, sy. 1 (Ocak 2022): 71-78. https://doi.org/10.25092/baunfbed.903026.
EndNote Kırmızı Çetinalp E (01 Ocak 2022) Regularity of n-generalized Schützenberger product of monoids. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24 1 71–78.
IEEE E. Kırmızı Çetinalp, “Regularity of n-generalized Schützenberger product of monoids”, BAUN Fen. Bil. Enst. Dergisi, c. 24, sy. 1, ss. 71–78, 2022, doi: 10.25092/baunfbed.903026.
ISNAD Kırmızı Çetinalp, Esra. “Regularity of N-Generalized Schützenberger Product of Monoids”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 24/1 (Ocak 2022), 71-78. https://doi.org/10.25092/baunfbed.903026.
JAMA Kırmızı Çetinalp E. Regularity of n-generalized Schützenberger product of monoids. BAUN Fen. Bil. Enst. Dergisi. 2022;24:71–78.
MLA Kırmızı Çetinalp, Esra. “Regularity of N-Generalized Schützenberger Product of Monoids”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, c. 24, sy. 1, 2022, ss. 71-78, doi:10.25092/baunfbed.903026.
Vancouver Kırmızı Çetinalp E. Regularity of n-generalized Schützenberger product of monoids. BAUN Fen. Bil. Enst. Dergisi. 2022;24(1):71-8.