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A Study of Congruence on (n, m)-semigroup

Received: 1 June 2017     Accepted: 29 June 2017     Published: 31 July 2017
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Abstract

Congruence is a special type of equivalence relation which plays a vital role in the study of quotient structures of different algebraic structures. The purpose of this paper is to study the quotient structure of (n, m)-semigroup by using the notion of congruence in (n, m)-semigroup. Firstly, the concept of homomorphism on (n, m)-semigroup is introduced. Then, the concept of congruence on (n, m)-semigroup is defined, and some basic properties are studied. Finally, it is proved that the set of congruences on an (n, m)-semigroup is a complete lattice. All these generalize the corresponding notions and results for usual binary and ternary semigroups.

Published in Pure and Applied Mathematics Journal (Volume 6, Issue 4)
DOI 10.11648/j.pamj.20170604.13
Page(s) 120-123
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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

(n, m)-semigroup, Homomorphism, Congruence

References
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[16] S. Kar and B. K. Maity. Congruences on ternary semigroups. Journal of the Chungcheong Mathematical Society, 2007, 20(3): 191-201.
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    Jiangping Xiao. (2017). A Study of Congruence on (n, m)-semigroup. Pure and Applied Mathematics Journal, 6(4), 120-123. https://doi.org/10.11648/j.pamj.20170604.13

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    ACS Style

    Jiangping Xiao. A Study of Congruence on (n, m)-semigroup. Pure Appl. Math. J. 2017, 6(4), 120-123. doi: 10.11648/j.pamj.20170604.13

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    AMA Style

    Jiangping Xiao. A Study of Congruence on (n, m)-semigroup. Pure Appl Math J. 2017;6(4):120-123. doi: 10.11648/j.pamj.20170604.13

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  • @article{10.11648/j.pamj.20170604.13,
      author = {Jiangping Xiao},
      title = {A Study of Congruence on (n, m)-semigroup},
      journal = {Pure and Applied Mathematics Journal},
      volume = {6},
      number = {4},
      pages = {120-123},
      doi = {10.11648/j.pamj.20170604.13},
      url = {https://doi.org/10.11648/j.pamj.20170604.13},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20170604.13},
      abstract = {Congruence is a special type of equivalence relation which plays a vital role in the study of quotient structures of different algebraic structures. The purpose of this paper is to study the quotient structure of (n, m)-semigroup by using the notion of congruence in (n, m)-semigroup. Firstly, the concept of homomorphism on (n, m)-semigroup is introduced. Then, the concept of congruence on (n, m)-semigroup is defined, and some basic properties are studied. Finally, it is proved that the set of congruences on an (n, m)-semigroup is a complete lattice. All these generalize the corresponding notions and results for usual binary and ternary semigroups.},
     year = {2017}
    }
    

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    Y1  - 2017/07/31
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    AB  - Congruence is a special type of equivalence relation which plays a vital role in the study of quotient structures of different algebraic structures. The purpose of this paper is to study the quotient structure of (n, m)-semigroup by using the notion of congruence in (n, m)-semigroup. Firstly, the concept of homomorphism on (n, m)-semigroup is introduced. Then, the concept of congruence on (n, m)-semigroup is defined, and some basic properties are studied. Finally, it is proved that the set of congruences on an (n, m)-semigroup is a complete lattice. All these generalize the corresponding notions and results for usual binary and ternary semigroups.
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    ER  - 

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Author Information
  • School of Mathematics Science, South China Normal University, Guangzhou, China

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