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

Year 2019, Volume: 68 Issue: 2, 1895 - 1908, 01.08.2019

Eylem Güzel Karpuz

https://doi.org/10.31801/cfsuasmas.472024
Cited By: 1

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.

Keywords

Automatic semigroup generalized Bruck-Reilly *-extension presentation

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, Volume: 68 Issue: 2, 1895 - 1908, 01.08.2019

Eylem Güzel Karpuz

https://doi.org/10.31801/cfsuasmas.472024
Cited By: 1

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 Volume: 68 Issue: 2

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.

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https://doi.org/10.25092/baunfbed.850352

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

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