Some algebraic properties of order-preserving full contraction transformation semigroup

G.R. Ibrahim, A.T. Imam, A.D. Adeshola, G.N. Bakare

Abstract


Let $X_{n}$ be a finite set, $CT_{n}$ the semigroup of full contraction and $OCT_{n}$ order-preserving full contraction transformation semigroup of a finite set. In this paper the Local and global U-depth as well as the status of $OCT_{n}$ were investigated where U is the generating set. The local and global depth were found from the known generating Set of $OCT_{n}$ and also, the status of the semigroup $OCT_{n}$ was obtained from the product of global depth and the order of generating of $OCT_{n}$. For $\alpha\in OCT_{n}$, local depth of α is equal to its defect, global depth and status of $OCT_{n}$ are $ n-1$ and $2(n-1)^{2}$ respectively. We also look at the structure of Green’s relations of order-preserving full contraction transformation semigroup.

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Published: 2019-01-04

How to Cite this Article:

G.R. Ibrahim, A.T. Imam, A.D. Adeshola, G.N. Bakare, Some algebraic properties of order-preserving full contraction transformation semigroup, Journal of Semigroup Theory and Applications, Vol 2019 (2019), Article ID 2

Copyright © 2019 G.R. Ibrahim, A.T. Imam, A.D. Adeshola, G.N. Bakare. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Journal of Semigroup Theory and Applications

ISSN 2051-2937

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