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Bir üçlü monoidin Bruck-Reilly genişlemesi

Year 2021, Volume: 23 Issue: 1, 252 - 258, 29.01.2021
https://doi.org/10.25092/baunfbed.850352

Abstract

Bu çalışmada bir üçlü monoidin Bruck-Reilly genişlemesi tanımlanmıştır. Ayrıca; regüler, tersinir, orthodox ve strongly regüler üçlü yarıgrup sınıflarından birine ait olan bu yapı ile ilgili bazı sonuçlar verilmiştir.

References

  • Bruck, R. H., A survey of binary systems, Ergebnisse der Mathematik, Neue Folge, Vol. 20, Springer, Berlin, (1958).
  • Reilly, N. R., Bisimple w-semigroups, Proc. Glasgow Math. Assoc., 7, 160-167, (1966).
  • Munn, W., On simple inverse semigroups, Semigroup Forum, 1, 63-74, (1970).
  • Asibong-Ibe, U., *-Bisimple type A w-semigroups-I, Semigroup Forum, 31, 99-117, (1985).
  • Howie, J. M., Ruskuc, N., Constructions and presentations for monoids, Comm. in Algebra, 22, 15, 6209-6224, (1994).
  • Karpuz, E. G., Çevik, A. S., Koppitz, J. and Cangül, İ. N., Some fixed-point results on (generalized) Bruck–Reilly ∗-extensions of monoids, Fixed Point Theory Appl., (2013).
  • Karpuz, E. G., Automatic structure for generalized Bruck-Reilly *-extension of a monoid, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68, 1895-1908 (2019).
  • Kocapinar,C., Karpuz, E. G., Ateş, F., Çevik,A. S., Gröbner-Shirshov bases of the generalized Bruck-Reilly _-extension, Algebra Colloquium, 19, 813-820, (2012).
  • Kochin, B. P., The structure of inverse ideal-simple w-semigroups, Vestnik Leningrad. Univ., 23,7, 41-50, (1968).
  • Munn, W., Regular w-semigroups, Glasgow Math. J., 9, 46-66, (1968).
  • Oğuz, S. and 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.
  • Oğuz, S., Special semigroup classes over some monoid constructions and a new example of a finitely presented monoid with a non-finitely generated group of units, Cumhuriyet University Faculty of Science Science Journal, 37, (2016)
  • Oğuz, S. and Karpuz, E. G., Finite presentability of generalized Bruck-Reilly *-extension of groups, Asian-European Journal of Mathematics, 9,4, (2016)
  • Piochi, B., Congruences on Bruck-Reilly extensions of monoids, Semigroup Forum, 50, 179-191, (1995).
  • Shung,Y., Wang, L. M., *-Bisimple type A w2-semigroups as generalized Bruck-Reilly -extensions, Southeast Asian Bulletin of Math., 32, 343-361, (2008).
  • Cayley, A., On the theory of linear transformations, Cambridge Math. J., 4, 193-209, (1845).
  • Lehmer, D.H, A ternary analogue of abelian groups, Amer jour of Math., 599, 329-338, (1932).
  • Los, J., On the extending of model I, Fund. Math., 42, 38-54, (1955).
  • Sioson, F.M., Ideal theory in ternary semigroups, Math. Japonica, 10, 63-84, (1965).
  • Santiago, M.L.: Regular ternary semigroups, Bull. Calcutta Math. Soc., 82, 67–71, (1990).
  • Sheeja G., Sri Bala, S., Orthodox ternary semigroups, Quasigroups and Related Systems, 19, 339 – 348, (2011).
  • Santiago, M. L. and Sri Bala,S., Ternary semigroups, Semigroup Forum, 81, 380− 388, (2010).
  • Kellil, R., Green's relations on ternary semigroups, Semigroup Theory Appl., 6, (2013).
  • Cliford, A. H., Preston, G. B., The algebraic theory of semigroups Volumes I and II, Mathematical Surveys, Number 7, AMS, (1964 - Vol. I), (1967 - Vol. II).
  • Howie, J. M., Fundamentals of semigroup theory, Clarendon Press-Oxford, (1995).

Bruck-Reilly extension of a ternary monoid

Year 2021, Volume: 23 Issue: 1, 252 - 258, 29.01.2021
https://doi.org/10.25092/baunfbed.850352

Abstract

In this study, Bruck-Reilly extension of a ternary monoid is defined. Additionally, some results about this construction are given which belongs to one of the classes of ternary semigroups; regular, inverse, orthodox and strongly regular.

References

  • Bruck, R. H., A survey of binary systems, Ergebnisse der Mathematik, Neue Folge, Vol. 20, Springer, Berlin, (1958).
  • Reilly, N. R., Bisimple w-semigroups, Proc. Glasgow Math. Assoc., 7, 160-167, (1966).
  • Munn, W., On simple inverse semigroups, Semigroup Forum, 1, 63-74, (1970).
  • Asibong-Ibe, U., *-Bisimple type A w-semigroups-I, Semigroup Forum, 31, 99-117, (1985).
  • Howie, J. M., Ruskuc, N., Constructions and presentations for monoids, Comm. in Algebra, 22, 15, 6209-6224, (1994).
  • Karpuz, E. G., Çevik, A. S., Koppitz, J. and Cangül, İ. N., Some fixed-point results on (generalized) Bruck–Reilly ∗-extensions of monoids, Fixed Point Theory Appl., (2013).
  • Karpuz, E. G., Automatic structure for generalized Bruck-Reilly *-extension of a monoid, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68, 1895-1908 (2019).
  • Kocapinar,C., Karpuz, E. G., Ateş, F., Çevik,A. S., Gröbner-Shirshov bases of the generalized Bruck-Reilly _-extension, Algebra Colloquium, 19, 813-820, (2012).
  • Kochin, B. P., The structure of inverse ideal-simple w-semigroups, Vestnik Leningrad. Univ., 23,7, 41-50, (1968).
  • Munn, W., Regular w-semigroups, Glasgow Math. J., 9, 46-66, (1968).
  • Oğuz, S. and 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.
  • Oğuz, S., Special semigroup classes over some monoid constructions and a new example of a finitely presented monoid with a non-finitely generated group of units, Cumhuriyet University Faculty of Science Science Journal, 37, (2016)
  • Oğuz, S. and Karpuz, E. G., Finite presentability of generalized Bruck-Reilly *-extension of groups, Asian-European Journal of Mathematics, 9,4, (2016)
  • Piochi, B., Congruences on Bruck-Reilly extensions of monoids, Semigroup Forum, 50, 179-191, (1995).
  • Shung,Y., Wang, L. M., *-Bisimple type A w2-semigroups as generalized Bruck-Reilly -extensions, Southeast Asian Bulletin of Math., 32, 343-361, (2008).
  • Cayley, A., On the theory of linear transformations, Cambridge Math. J., 4, 193-209, (1845).
  • Lehmer, D.H, A ternary analogue of abelian groups, Amer jour of Math., 599, 329-338, (1932).
  • Los, J., On the extending of model I, Fund. Math., 42, 38-54, (1955).
  • Sioson, F.M., Ideal theory in ternary semigroups, Math. Japonica, 10, 63-84, (1965).
  • Santiago, M.L.: Regular ternary semigroups, Bull. Calcutta Math. Soc., 82, 67–71, (1990).
  • Sheeja G., Sri Bala, S., Orthodox ternary semigroups, Quasigroups and Related Systems, 19, 339 – 348, (2011).
  • Santiago, M. L. and Sri Bala,S., Ternary semigroups, Semigroup Forum, 81, 380− 388, (2010).
  • Kellil, R., Green's relations on ternary semigroups, Semigroup Theory Appl., 6, (2013).
  • Cliford, A. H., Preston, G. B., The algebraic theory of semigroups Volumes I and II, Mathematical Surveys, Number 7, AMS, (1964 - Vol. I), (1967 - Vol. II).
  • Howie, J. M., Fundamentals of semigroup theory, Clarendon Press-Oxford, (1995).
There are 25 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Seda Oğuz Ünal This is me 0000-0003-1338-1466

Publication Date January 29, 2021
Submission Date June 23, 2020
Published in Issue Year 2021 Volume: 23 Issue: 1

Cite

APA Oğuz Ünal, S. (2021). Bruck-Reilly extension of a ternary monoid. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 23(1), 252-258. https://doi.org/10.25092/baunfbed.850352
AMA Oğuz Ünal S. Bruck-Reilly extension of a ternary monoid. BAUN Fen. Bil. Enst. Dergisi. January 2021;23(1):252-258. doi:10.25092/baunfbed.850352
Chicago Oğuz Ünal, Seda. “Bruck-Reilly Extension of a Ternary Monoid”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23, no. 1 (January 2021): 252-58. https://doi.org/10.25092/baunfbed.850352.
EndNote Oğuz Ünal S (January 1, 2021) Bruck-Reilly extension of a ternary monoid. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23 1 252–258.
IEEE S. Oğuz Ünal, “Bruck-Reilly extension of a ternary monoid”, BAUN Fen. Bil. Enst. Dergisi, vol. 23, no. 1, pp. 252–258, 2021, doi: 10.25092/baunfbed.850352.
ISNAD Oğuz Ünal, Seda. “Bruck-Reilly Extension of a Ternary Monoid”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi 23/1 (January 2021), 252-258. https://doi.org/10.25092/baunfbed.850352.
JAMA Oğuz Ünal S. Bruck-Reilly extension of a ternary monoid. BAUN Fen. Bil. Enst. Dergisi. 2021;23:252–258.
MLA Oğuz Ünal, Seda. “Bruck-Reilly Extension of a Ternary Monoid”. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 23, no. 1, 2021, pp. 252-8, doi:10.25092/baunfbed.850352.
Vancouver Oğuz Ünal S. Bruck-Reilly extension of a ternary monoid. BAUN Fen. Bil. Enst. Dergisi. 2021;23(1):252-8.