Science Journal of Applied Mathematics and Statistics
Volume 5, Issue 3, June 2017, Pages: 106-109
Received: Feb. 17, 2017;
Accepted: Apr. 20, 2017;
Published: Jun. 1, 2017
Views 1738 Downloads 87
Nosratollah Shajareh Poursalavati, Department of Pure Mathematics, Faculty of Mathematics and Computer, Mahani Mathematical Research Center, Shahid Bahonar University of Kerman, Kerman, Iran
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.
Nosratollah Shajareh Poursalavati,
On the Construction of Molaei’s Generalized Hypergroups, Science Journal of Applied Mathematics and Statistics.
Vol. 5, No. 3,
2017, pp. 106-109.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
H. Aghabozorgi, B. Davvaz and M. Jafarpour, Solvable polygroups and derived subpolygroups, Communications in Algebra, 41(8) (2013) 3098-3107.
S. D. Comer, Polygroups derived from cogroups, J. Algebra, 89 (1984) 397-405.
P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore, 1993.
B. Davvaz, Isomorphism theorems of polygroups, Bull. Malays. Math. Sci. Soc. (2), 33(3) (2010) 385-392.
B. Davvaz, Polygroup Theory and Related Systems, World Scienti_c Publishing Co. Pte. Ltd., Hackensack, NJ, 2013.
M. Jafarpour, H. Aghabozorgi and B. Davvaz, On nilpotent and solvable polygroups, Bulletin of Iranian Mathematical Society, 39(3) (2013) 487-499.
J. M. Howie, Fundamentals of semigroup theory, Oxford University Press, New York, 1995.
F. Marty, Sur une generalization de la notion de groupe, 8iem congres Math. Scandinaves, Stockholm, (1934) 45-49.
M. R. Molaei, Generalized groups, Bulet. Inst. Politehn. Ia¸si Sect,. I, 45(49) (1999) 21-24.