A Study of Congruence on (<i>n, m</i>)-semigroup

Jiangping Xiao

doi:doi:10.11648/j.pamj.20170604.13

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

Jiangping Xiao

Published in Pure and Applied Mathematics Journal (Volume 6, Issue 4)

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
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

(n, m)-semigroup, Homomorphism, Congruence

References

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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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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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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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TY  - JOUR
T1  - A Study of Congruence on (n, m)-semigroup
AU  - Jiangping Xiao
Y1  - 2017/07/31
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170604.13
DO  - 10.11648/j.pamj.20170604.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 120
EP  - 123
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20170604.13
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.
VL  - 6
IS  - 4
ER  -

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Author Information

Jiangping Xiao

School of Mathematics Science, South China Normal University, Guangzhou, China

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APA Style

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
T1  - A Study of Congruence on (n, m)-semigroup
AU  - Jiangping Xiao
Y1  - 2017/07/31
PY  - 2017
N1  - https://doi.org/10.11648/j.pamj.20170604.13
DO  - 10.11648/j.pamj.20170604.13
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 120
EP  - 123
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20170604.13
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.
VL  - 6
IS  - 4
ER  -

Copy | Download