Some Structures of Hemirings
Pure and Applied Mathematics Journal
Volume 6, Issue 1, February 2017, Pages: 45-50
Received: Jan. 27, 2017; Accepted: Feb. 8, 2017; Published: Mar. 1, 2017
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Md. Yasin Ali, School of Science and Engineering, University of Information Technology & Sciences, Dhaka, Bangladesh; Department of Mathematics, Jahangirnagar University, Savar, Bangladesh
Kanak Ray Chowdhury, Department of Mathematics, Mohammadpur Model School and College, Mohammadpur, Dhaka, Bangladesh
Abeda Sultana, Department of Mathematics, Jahangirnagar University, Savar, Bangladesh
Nirmal Kanti Mitra, Mathematical and Physical Sciences, Bangladesh University of Business and Technology, Dhaka, Bangladesh
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Hemirings appear in a natural manner, in some applications to the theory of automata, the theory of formal languages, graph theory, design theory and combinatorial geometry. Recently, the notions of hemirings with special structures were introduced. But still now there are no complete structural properties of hemirings. In this paper we try to investigate some structures of hemirings. This is done by introducing some examples of hemirings.
Hemirings, Zerosumfree Hemirings, Simple Hemirings
To cite this article
Md. Yasin Ali, Kanak Ray Chowdhury, Abeda Sultana, Nirmal Kanti Mitra, Some Structures of Hemirings, Pure and Applied Mathematics Journal. Vol. 6, No. 1, 2017, pp. 45-50. doi: 10.11648/j.pamj.20170601.16
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
J. S. Golan, “Semirings and Their Applications”, Kluwer Acad. Publ. (1999).
J. S. Golan, “Semirings and Affine Equations over Them: Theory and Applications” Kluwer Academic Publishers (1999).
U. Hebisch and H. J. Weinert, “Semirings: Algebraic Theory and Applications in theComputer Science”, World Scientific, 1998.
Jianming Zhan, Wiesław A. Dudek, “Fuzzy h-ideals of hemirings”, Information Sciences 177 (2007), pp. 876–886.
J. N. Mordeson and D. S. Malik, “Fuzzy Automata and Languages, Theory and Applications”, Computational Mathematics Series, Chapman and Hall/CRC, Boca Raton 2002.
Muhammad Shabir, Nosheen Malik, Tahir Mahmood, “Characterizations of hemirings by The properties of their interval valued fuzzy Ideals”, Annals of Fuzzy Mathematics and Informatics 3 (2), (April 2012), pp. 229-242.
M. Gulistan, M. Shahzad, S. Ahmed and M. Ilyas, “Characterization of Gamma Hemirings By Generalized Fuzzy Gamma Ideals”, Application and Applied Mathematics, Vol. 10. Issue 1 (June 2015), pp. 495-520.
Huajun Wu and Jianming Zhan, “Soft Hemiring Related to Fuzzy Set Theory” KYUNGPOOK Math. J. 52 (2012), pp. 61-79.
K. Ray Chowdhury, Md. Yasin Ali, A. Sultana, N. K. Mitra and A. F. M. Khodadad Khan, “On Matrices Over Path Algebra”, Annals of Pure and Applied Mathematics 11 (2), 2016, pp. 45-55.
Y. Q. Yin and H. X. Li, “The Characterizations of h-hemiregular hemirings and h-intra hemirings”, Inform. Sci. 178 (2008) pp. 3451–3464.
Huajun Wu, Jianming Zhan, “The characterizations of some kinds of soft hemirings”, Annals of Fuzzy Mathematics and Informatics 3 (2), (April 2012), pp. 267- 280.
K. Ray Chowdhury, A. Sultana, N. K. Mitraand A. F. M. Khodadad Khan, “Some Structural Properties of Semirings”, Annals of Pure and Applied Mathematics, 5 (2) (2014) pp. 158-167.
W. A. Dudek, M. Shabir and M. Irfan Ali, “ fuzzy ideals of hemirings”, Comput. Math. Appl. 58 (2009) pp. 310–321.
Muhammad Shabir and Tahir Mahmood,“Hemirings characterized by the properties of their fuzzy ideals with thresholds”, Quasigroups and Related Systems 18 (2010), pp. 195–212.
D. R. La Torre, “On h-ideals and k-ideals in Hemirings”, Publ. Math. Debrecen, 12 (2), pp. 219-226, 1965.
W. A. Dudek, “Special types of intuitionistic fuzzy left h-ideals of hemirings”, Soft Comput., 12 (4), pp. 359-364, 2008.
M. Zhou and S. li, “Application of bipolar fuzzy theory to hemiring”, International Journal of Innovative Computing, Information and Control Volume 10 (2), April, 2014, pp 767-781.
N. Sulochana and T. Vasanthi, “Structure of Some Idempotent Semirings”, Journal of Computer and Mathematical Science, Vol, 7 (5), pp. 294-301, 2016.
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