On the Construction of Molaei’s Generalized Hypergroups

Nosratollah Shajareh Poursalavati

doi:doi:10.11648/j.sjams.20170503.12

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On the Construction of Molaei’s Generalized Hypergroups

Nosratollah Shajareh Poursalavati

Published in Science Journal of Applied Mathematics and Statistics (Volume 5, Issue 3)

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), 2024. 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.

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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},
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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.},
 year = {2017}
}

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TY  - JOUR
T1  - On the Construction of Molaei’s Generalized Hypergroups
AU  - Nosratollah Shajareh Poursalavati
Y1  - 2017/06/01
PY  - 2017
N1  - https://doi.org/10.11648/j.sjams.20170503.12
DO  - 10.11648/j.sjams.20170503.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - 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

Nosratollah Shajareh Poursalavati

Department of Pure Mathematics, Faculty of Mathematics and Computer, Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran

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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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - On the Construction of Molaei’s Generalized Hypergroups
AU  - Nosratollah Shajareh Poursalavati
Y1  - 2017/06/01
PY  - 2017
N1  - https://doi.org/10.11648/j.sjams.20170503.12
DO  - 10.11648/j.sjams.20170503.12
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 106
EP  - 109
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20170503.12
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
IS  - 3
ER  -

Copy | Download