IJPAM: Volume 99, No. 3 (2015)

THE PARTIAL ORDER ON CATEGORY OF
SEMIGROUPS AND ENDO-CAYLEY DIGRAPHS

C. Promsakon
Department of Mathematics
Faculty of Applied Sciences
King Mongkul's University of Technology North Bangkok
Bangkok, THAILAND


Abstract. Let $\mathbb C$ be a set of all structures $(S_f,A)$ where $S$ is a semigroup, $f$ is an endomorphism on $S$ and $A$ is a subset of $S$. We define operation $\otimes$ on $\mathbb C$ and also prove $(\mathbb C,\otimes)$ is a semigroup. Similarly, we show $\mathbb D$, the set of all endo-Caylay sigraphs, is a semigroup under the tensor product. Moreover, we find partial order relations in both $\mathbb C$ and $\mathbb D$.

Received: July 30, 2014

AMS Subject Classification: 06F05, 05C60, 05C76

Key Words and Phrases: Endo-Cayley digraph, partial order, semigroups

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DOI: 10.12732/ijpam.v99i3.2 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 99
Issue: 3
Pages: 245 - 255


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CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).