Abstract

ON SEMIGROUPS OF PARTIAL CONTRACTIONS OF A FINITE CHAIN

Musa BALARABE1, Abdussamad Tanko IMAM1 and Oladapo Ade

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Abstract Let X_n = {1,2,...,n} be the finite n-elements set under its natural order. A partial map ? of X_n is said to be a contraction if, for all x,y? dom(?), |x? -y?| ? |x -y| and an order-preserving if, x,y? dom(?), x ? y ? x? ? y?. Let ?CP?_n and ?OCP?_n denote, respectively, semigroups of all partial contraction maps and of all order preserving partial contraction maps. In this paper, we study the structure of ?CP?_n and ?OCP?_n and present characterisations of starred Green?s relations in these semigroups. Keywords. Order-preserving map, Contraction map, Green?s relations, Starred Green?s relations.

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