Some Structures of Hemirings

Md. Yasin Ali; Kanak Ray Chowdhury; Abeda Sultana; Nirmal Kanti Mitra

doi:doi:10.11648/j.pamj.20170601.16

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Some Structures of Hemirings

Md. Yasin Ali, Kanak Ray Chowdhury, Abeda Sultana, Nirmal Kanti Mitra

Published in Pure and Applied Mathematics Journal (Volume 6, Issue 1)

Received: 27 January 2017 Accepted: 8 February 2017 Published: 1 March 2017

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Abstract

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.

Published in	Pure and Applied Mathematics Journal (Volume 6, Issue 1)
DOI	10.11648/j.pamj.20170601.16
Page(s)	45-50
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

Hemirings, Zerosumfree Hemirings, Simple Hemirings

References

[1]	J. S. Golan, “Semirings and Their Applications”, Kluwer Acad. Publ. (1999).
[2]	J. S. Golan, “Semirings and Affine Equations over Them: Theory and Applications” Kluwer Academic Publishers (1999).
[3]	U. Hebisch and H. J. Weinert, “Semirings: Algebraic Theory and Applications in theComputer Science”, World Scientific, 1998.
[4]	Jianming Zhan, Wiesław A. Dudek, “Fuzzy h-ideals of hemirings”, Information Sciences 177 (2007), pp. 876–886.
[5]	J. N. Mordeson and D. S. Malik, “Fuzzy Automata and Languages, Theory and Applications”, Computational Mathematics Series, Chapman and Hall/CRC, Boca Raton 2002.
[6]	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.
[7]	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.
[8]	Huajun Wu and Jianming Zhan, “Soft Hemiring Related to Fuzzy Set Theory” KYUNGPOOK Math. J. 52 (2012), pp. 61-79.
[9]	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.
[10]	Y. Q. Yin and H. X. Li, “The Characterizations of h-hemiregular hemirings and h-intra hemirings”, Inform. Sci. 178 (2008) pp. 3451–3464.
[11]	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.
[12]	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.
[13]	W. A. Dudek, M. Shabir and M. Irfan Ali, “ fuzzy ideals of hemirings”, Comput. Math. Appl. 58 (2009) pp. 310–321.
[14]	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.
[15]	D. R. La Torre, “On h-ideals and k-ideals in Hemirings”, Publ. Math. Debrecen, 12 (2), pp. 219-226, 1965.
[16]	W. A. Dudek, “Special types of intuitionistic fuzzy left h-ideals of hemirings”, Soft Comput., 12 (4), pp. 359-364, 2008.
[17]	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.
[18]	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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APA Style

Md. Yasin Ali, Kanak Ray Chowdhury, Abeda Sultana, Nirmal Kanti Mitra. (2017). Some Structures of Hemirings. Pure and Applied Mathematics Journal, 6(1), 45-50. https://doi.org/10.11648/j.pamj.20170601.16

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ACS Style

Md. Yasin Ali; Kanak Ray Chowdhury; Abeda Sultana; Nirmal Kanti Mitra. Some Structures of Hemirings. Pure Appl. Math. J. 2017, 6(1), 45-50. doi: 10.11648/j.pamj.20170601.16

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AMA Style

Md. Yasin Ali, Kanak Ray Chowdhury, Abeda Sultana, Nirmal Kanti Mitra. Some Structures of Hemirings. Pure Appl Math J. 2017;6(1):45-50. doi: 10.11648/j.pamj.20170601.16

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@article{10.11648/j.pamj.20170601.16,
  author = {Md. Yasin Ali and Kanak Ray Chowdhury and Abeda Sultana and Nirmal Kanti Mitra},
  title = {Some Structures of Hemirings},
  journal = {Pure and Applied Mathematics Journal},
  volume = {6},
  number = {1},
  pages = {45-50},
  doi = {10.11648/j.pamj.20170601.16},
  url = {https://doi.org/10.11648/j.pamj.20170601.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170601.16},
  abstract = {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.},
 year = {2017}
}

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TY  - JOUR
T1  - Some Structures of Hemirings
AU  - Md. Yasin Ali
AU  - Kanak Ray Chowdhury
AU  - Abeda Sultana
AU  - Nirmal Kanti Mitra
Y1  - 2017/03/01
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170601.16
DO  - 10.11648/j.pamj.20170601.16
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 45
EP  - 50
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20170601.16
AB  - 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.
VL  - 6
IS  - 1
ER  -

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Author Information

Md. Yasin Ali

School of Science and Engineering, University of Information Technology & Sciences, Dhaka, 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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APA Style

Md. Yasin Ali, Kanak Ray Chowdhury, Abeda Sultana, Nirmal Kanti Mitra. (2017). Some Structures of Hemirings. Pure and Applied Mathematics Journal, 6(1), 45-50. https://doi.org/10.11648/j.pamj.20170601.16

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ACS Style

Md. Yasin Ali; Kanak Ray Chowdhury; Abeda Sultana; Nirmal Kanti Mitra. Some Structures of Hemirings. Pure Appl. Math. J. 2017, 6(1), 45-50. doi: 10.11648/j.pamj.20170601.16

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AMA Style

Md. Yasin Ali, Kanak Ray Chowdhury, Abeda Sultana, Nirmal Kanti Mitra. Some Structures of Hemirings. Pure Appl Math J. 2017;6(1):45-50. doi: 10.11648/j.pamj.20170601.16

Copy | Download

@article{10.11648/j.pamj.20170601.16,
  author = {Md. Yasin Ali and Kanak Ray Chowdhury and Abeda Sultana and Nirmal Kanti Mitra},
  title = {Some Structures of Hemirings},
  journal = {Pure and Applied Mathematics Journal},
  volume = {6},
  number = {1},
  pages = {45-50},
  doi = {10.11648/j.pamj.20170601.16},
  url = {https://doi.org/10.11648/j.pamj.20170601.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170601.16},
  abstract = {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.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Some Structures of Hemirings
AU  - Md. Yasin Ali
AU  - Kanak Ray Chowdhury
AU  - Abeda Sultana
AU  - Nirmal Kanti Mitra
Y1  - 2017/03/01
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170601.16
DO  - 10.11648/j.pamj.20170601.16
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 45
EP  - 50
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20170601.16
AB  - 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.
VL  - 6
IS  - 1
ER  -

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