SavedAdd your journal

Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Volume: 68 Issue: 2

Automatic structure for generalized Bruck-Reilly ∗-extension of a monoid

Eylem Güzel Karpuz(KARAMANOGLU MEHMETBEY UNIVERSITY)0000-0002-7111-3462
Pages
—
Publication Date
2019-08-01
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Under some certain situations, we prove that the automaticity of the monoid implies the automaticity of the generalized Bruck-Reilly ∗-extension of this monoid.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In the present paper, we study the automaticity of generalized Bruck-Reilly ∗-extension of a monoid.
📊
Key Findings & Data:In the present paper, we study the automaticity of generalized Bruck-Reilly ∗-extension of a monoid.
💡
Conclusion & Impact:Under some certain situations, we prove that the automaticity of the monoid implies the automaticity of the generalized Bruck-Reilly ∗-extension of this monoid.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Automatic semigroup · generalized Bruck-Reilly *-extension · presentation

Abstract

In the present paper, we study the automaticity of generalized Bruck-Reilly ∗-extension of a monoid. Under some certain situations, we prove that the automaticity of the monoid implies the automaticity of the generalized Bruck-Reilly ∗-extension of this monoid.

🔖

Cite This Article

Karpuz, E. G. (2019). Automatic structure for generalized Bruck-Reilly ∗-extension of a monoid. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 2. https://doi.org/10.31801/cfsuasmas.472024

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (20)

  1. Andrade, L., Descalço, L., Martins, M. A., Automatic structures for semigroup constructions, Semigroup Forum, 76(2) (2008) 239-255.
  2. Asibong-Ibe, U., -Bisimple type A w-semigroups-I, Semigroup Forum, 31 (1985) 99-117.
  3. Cain, A. J., Automatic semigroups and Bruck-Reilly extensions, Acta Math. Hungar., 126(1-2) (2010) 1-15.
  4. Campbell, C. M., Robertson, E. F., Ruskuc, N., Thomas, R. M., Direct products of automatic semigroups, J. Austral. Math. Soc. Ser. A, 69 (2000) 19-24.
  5. Campbell, C. M., Robertson, E. F., Ruskuc, N., Thomas, R. M., Automatic semigroups, Theoretical Computer Science, 250 (2001) 365-391.
  6. Descalço, L., Automatic semigroups: Constructions and subsemigroups, Ph.D. Thesis, University of St Andrews, 2002.
  7. Descalço, L., Ruskuc, N., On automatic Rees matrix semigroups, Comm. Algebra, 30 (2002) 1207-1226.
  8. Epstein, D. B. A., Cannon, J. W., Holt, D. F., Levy, S. V. F., Paterson, M. S. and Thurston, W. P., Word Processing in Groups, Jones & Bartlett (Boston, Mass.), 1992.
  9. Hoffmann, M., Automatic Semigroups, Ph.D. Thesis, University of Leicester, 2001.
  10. Hoffmann, M., Thomas, R. M., Automaticity and commutative semigroups, Glasgow J.Math., 44 (2002) 167-176.
  11. Hudson, J. F. P., Regular rewrite systems and automatic structures, in J. Almeida, G. M. S. Gomes and P. V. Silva, edts, Semigroups, Automata and Languages, World Scienti c, Singapore, 1996, pp. 145-152.
  12. Karpuz, E. G., Çevik, A. S., Koppitz, J., Cangül, I. N., Some fi xed-point results on (generalized) Bruck-Reilly *-extensions of monoids, Fixed Point Theory and Applications, (2013) 2013: 78, doi: 10.1186/1687-1812-2013-78.
  13. Kocapinar, C., Karpuz, E., G., Ateş, F. and Çevik, A. S., Gröbner-Shirshov bases of the generalized Bruck-Reilly *-extension, Algebra Colloquium, 19 (Spec1) (2012) 813-820.
  14. Oguz, S., Karpuz, E. G., Some semigroup classes and congruences on Bruck-Reilly and generalized Bruck-Reilly *-extensions of monoids, Asian-European Journal of Mathematics, 8(4) (2015) DOI: 10.1142/S1793557115500758.
  15. Oguz, S., Karpuz, E. G., Finite presentability of generalized Bruck-Reilly *-extension of groups, Asian-European Journal of Mathematics, 9(4) (2016).
  16. Otto, F., On s-regular pre x-rewriting systems and automatic structures, Computing and Combinatories (Tokyo, 1999), Lecture Notes in Comput. Sci., 1627, Springer, Berlin, 1999, pp. 422-431.
  17. Otto, F., On Dehn functions of fi nitely presented bi-automatic monoids, J. Austom. Lang. Comb., 5 (2000) 405-419.
  18. Otto, F., Sattler-Klein, A. and Madlener, K., Automatic monoids versus monoids with fi nite convergent presentations, Rewriting Techniques and Applications (Tsukuba, 1998), Lecture Notes in Comput. Sci., 1379, Springer, Berlin, 1998, pp. 32-46.
  19. Shang, Y., Wang, L. M., *-Bisimple type A w2-semigroups as generalized Bruck-Reilly *-extensions, Southeast Asian Bulletin of Math., 32 (2008) 343-361.
  20. Silva, P. V., Steinberg, B., A geometric characterization of automatic monoids, Quart. J. Math., 55 (2004) 333-356.