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On the Construction of Molaei’s Generalized Hypergroups

Received: 17 February 2017     Accepted: 20 April 2017     Published: 1 June 2017
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Abstract

The purpose of this paper is making a construction and generalization of Molaei’s generalized groups by using construction of the Rees matrix semigroup over a polygroup H and a matrix with entries in H. We call it “Molaei’s generalized hypergroups” and we give some examples.

Published in Science Journal of Applied Mathematics and Statistics (Volume 5, Issue 3)
DOI 10.11648/j.sjams.20170503.12
Page(s) 106-109
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Hypergroup, Polygroup, Molaei’s Generalized Hypergroup

References
[1] J. Aaújo and J. Konieczny, Molaei’s generalized groups are completely simple semigroups, Bul. Inst. Politeh. Jassy, Sect. I. Mat. Mec. Teor. Fiz. 48(52) (2002) 1-5.
[2] H. Aghabozorgi, B. Davvaz and M. Jafarpour, Solvable polygroups and derived subpolygroups, Communications in Algebra, 41(8) (2013) 3098-3107.
[3] S. D. Comer, Polygroups derived from cogroups, J. Algebra, 89 (1984) 397-405.
[4] P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, 1993.
[5] B. Davvaz, Isomorphism theorems of polygroups, Bull. Malays. Math. Sci. Soc. (2), 33(3) (2010) 385-392.
[6] B. Davvaz, Polygroup Theory and Related Systems, World Scienti_c Publishing Co. Pte. Ltd., Hackensack, NJ, 2013.
[7] M. Jafarpour, H. Aghabozorgi and B. Davvaz, On nilpotent and solvable polygroups, Bulletin of Iranian Mathematical Society, 39(3) (2013) 487-499.
[8] J. M. Howie, Fundamentals of semigroup theory, Oxford University Press, New York, 1995.
[9] F. Marty, Sur une generalization de la notion de groupe, 8iem congres Math. Scandinaves, Stockholm, (1934) 45-49.
[10] M. R. Molaei, Generalized groups, Bulet. Inst. Politehn. Ia¸si Sect,. I, 45(49) (1999) 21-24.
Cite This Article
  • APA Style

    Nosratollah Shajareh Poursalavati. (2017). On the Construction of Molaei’s Generalized Hypergroups. Science Journal of Applied Mathematics and Statistics, 5(3), 106-109. https://doi.org/10.11648/j.sjams.20170503.12

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    ACS Style

    Nosratollah Shajareh Poursalavati. On the Construction of Molaei’s Generalized Hypergroups. Sci. J. Appl. Math. Stat. 2017, 5(3), 106-109. doi: 10.11648/j.sjams.20170503.12

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    AMA Style

    Nosratollah Shajareh Poursalavati. On the Construction of Molaei’s Generalized Hypergroups. Sci J Appl Math Stat. 2017;5(3):106-109. doi: 10.11648/j.sjams.20170503.12

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  • @article{10.11648/j.sjams.20170503.12,
      author = {Nosratollah Shajareh Poursalavati},
      title = {On the Construction of Molaei’s Generalized Hypergroups},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {5},
      number = {3},
      pages = {106-109},
      doi = {10.11648/j.sjams.20170503.12},
      url = {https://doi.org/10.11648/j.sjams.20170503.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20170503.12},
      abstract = {The purpose of this paper is making a construction and generalization of Molaei’s generalized groups by using construction of the Rees matrix semigroup over a polygroup H and a matrix with entries in H. We call it “Molaei’s generalized hypergroups” and we give some examples.},
     year = {2017}
    }
    

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    Y1  - 2017/06/01
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    DO  - 10.11648/j.sjams.20170503.12
    T2  - Science Journal of Applied Mathematics and Statistics
    JF  - Science Journal of Applied Mathematics and Statistics
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    AB  - The purpose of this paper is making a construction and generalization of Molaei’s generalized groups by using construction of the Rees matrix semigroup over a polygroup H and a matrix with entries in H. We call it “Molaei’s generalized hypergroups” and we give some examples.
    VL  - 5
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Author Information
  • Department of Pure Mathematics, Faculty of Mathematics and Computer, Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran

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