A Study of Congruence on (n, m)-semigroup
Pure and Applied Mathematics Journal
Volume 6, Issue 4, August 2017, Pages: 120-123
Received: Jun. 1, 2017; Accepted: Jun. 29, 2017; Published: Jul. 31, 2017
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Author
Jiangping Xiao, School of Mathematics Science, South China Normal University, Guangzhou, China
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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.
Keywords
(n, m)-semigroup, Homomorphism, Congruence
To cite this article
Jiangping Xiao, A Study of Congruence on (n, m)-semigroup, Pure and Applied Mathematics Journal. Vol. 6, No. 4, 2017, pp. 120-123. doi: 10.11648/j.pamj.20170604.13
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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.
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