Research Article
BibTex RIS Cite

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

Year 2019, , 1895 - 1908, 01.08.2019
https://doi.org/10.31801/cfsuasmas.472024

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.

References

  • Andrade, L., Descalço, L., Martins, M. A., Automatic structures for semigroup constructions, Semigroup Forum, 76(2) (2008) 239-255.
  • Asibong-Ibe, U., -Bisimple type A w-semigroups-I, Semigroup Forum, 31 (1985) 99-117.
  • Cain, A. J., Automatic semigroups and Bruck-Reilly extensions, Acta Math. Hungar., 126(1-2) (2010) 1-15.
  • 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.
  • Campbell, C. M., Robertson, E. F., Ruskuc, N., Thomas, R. M., Automatic semigroups, Theoretical Computer Science, 250 (2001) 365-391.
  • Descalço, L., Automatic semigroups: Constructions and subsemigroups, Ph.D. Thesis, University of St Andrews, 2002.
  • Descalço, L., Ruskuc, N., On automatic Rees matrix semigroups, Comm. Algebra, 30 (2002) 1207-1226.
  • 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.
  • Hoffmann, M., Automatic Semigroups, Ph.D. Thesis, University of Leicester, 2001.
  • Hoffmann, M., Thomas, R. M., Automaticity and commutative semigroups, Glasgow J.Math., 44 (2002) 167-176.
  • 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.
  • 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.
  • 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.
  • 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.
  • Oguz, S., Karpuz, E. G., Finite presentability of generalized Bruck-Reilly *-extension of groups, Asian-European Journal of Mathematics, 9(4) (2016).
  • 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.
  • Otto, F., On Dehn functions of fi nitely presented bi-automatic monoids, J. Austom. Lang. Comb., 5 (2000) 405-419.
  • 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.
  • Shang, Y., Wang, L. M., *-Bisimple type A w2-semigroups as generalized Bruck-Reilly *-extensions, Southeast Asian Bulletin of Math., 32 (2008) 343-361.
  • Silva, P. V., Steinberg, B., A geometric characterization of automatic monoids, Quart. J. Math., 55 (2004) 333-356.
Year 2019, , 1895 - 1908, 01.08.2019
https://doi.org/10.31801/cfsuasmas.472024

Abstract

References

  • Andrade, L., Descalço, L., Martins, M. A., Automatic structures for semigroup constructions, Semigroup Forum, 76(2) (2008) 239-255.
  • Asibong-Ibe, U., -Bisimple type A w-semigroups-I, Semigroup Forum, 31 (1985) 99-117.
  • Cain, A. J., Automatic semigroups and Bruck-Reilly extensions, Acta Math. Hungar., 126(1-2) (2010) 1-15.
  • 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.
  • Campbell, C. M., Robertson, E. F., Ruskuc, N., Thomas, R. M., Automatic semigroups, Theoretical Computer Science, 250 (2001) 365-391.
  • Descalço, L., Automatic semigroups: Constructions and subsemigroups, Ph.D. Thesis, University of St Andrews, 2002.
  • Descalço, L., Ruskuc, N., On automatic Rees matrix semigroups, Comm. Algebra, 30 (2002) 1207-1226.
  • 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.
  • Hoffmann, M., Automatic Semigroups, Ph.D. Thesis, University of Leicester, 2001.
  • Hoffmann, M., Thomas, R. M., Automaticity and commutative semigroups, Glasgow J.Math., 44 (2002) 167-176.
  • 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.
  • 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.
  • 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.
  • 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.
  • Oguz, S., Karpuz, E. G., Finite presentability of generalized Bruck-Reilly *-extension of groups, Asian-European Journal of Mathematics, 9(4) (2016).
  • 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.
  • Otto, F., On Dehn functions of fi nitely presented bi-automatic monoids, J. Austom. Lang. Comb., 5 (2000) 405-419.
  • 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.
  • Shang, Y., Wang, L. M., *-Bisimple type A w2-semigroups as generalized Bruck-Reilly *-extensions, Southeast Asian Bulletin of Math., 32 (2008) 343-361.
  • Silva, P. V., Steinberg, B., A geometric characterization of automatic monoids, Quart. J. Math., 55 (2004) 333-356.
There are 20 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Review Articles
Authors

Eylem Güzel Karpuz 0000-0002-7111-3462

Publication Date August 1, 2019
Submission Date October 18, 2018
Acceptance Date February 28, 2019
Published in Issue Year 2019

Cite

APA Güzel Karpuz, E. (2019). Automatic structure for generalized Bruck-Reilly ∗-extension of a monoid. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(2), 1895-1908. https://doi.org/10.31801/cfsuasmas.472024
AMA Güzel Karpuz E. Automatic structure for generalized Bruck-Reilly ∗-extension of a monoid. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2019;68(2):1895-1908. doi:10.31801/cfsuasmas.472024
Chicago Güzel Karpuz, Eylem. “Automatic Structure for Generalized Bruck-Reilly ∗-Extension of a Monoid”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 2 (August 2019): 1895-1908. https://doi.org/10.31801/cfsuasmas.472024.
EndNote Güzel Karpuz E (August 1, 2019) Automatic structure for generalized Bruck-Reilly ∗-extension of a monoid. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 2 1895–1908.
IEEE E. Güzel Karpuz, “Automatic structure for generalized Bruck-Reilly ∗-extension of a monoid”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1895–1908, 2019, doi: 10.31801/cfsuasmas.472024.
ISNAD Güzel Karpuz, Eylem. “Automatic Structure for Generalized Bruck-Reilly ∗-Extension of a Monoid”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/2 (August 2019), 1895-1908. https://doi.org/10.31801/cfsuasmas.472024.
JAMA Güzel Karpuz E. Automatic structure for generalized Bruck-Reilly ∗-extension of a monoid. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:1895–1908.
MLA Güzel Karpuz, Eylem. “Automatic Structure for Generalized Bruck-Reilly ∗-Extension of a Monoid”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 2, 2019, pp. 1895-08, doi:10.31801/cfsuasmas.472024.
Vancouver Güzel Karpuz E. Automatic structure for generalized Bruck-Reilly ∗-extension of a monoid. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(2):1895-908.

Cited By

Bruck-Reilly extension of a ternary monoid
Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
https://doi.org/10.25092/baunfbed.850352

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.