REGULARITY OF TRANSFORMATION SEMIGROUPS DEFINED BY A PARTITION

- Journal title : Communications of the Korean Mathematical Society
- Volume 31, Issue 2, 2016, pp.217-227
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2016.31.2.217

Title & Authors

REGULARITY OF TRANSFORMATION SEMIGROUPS DEFINED BY A PARTITION

Purisang, Pattama; Rakbud, Jittisak;

Purisang, Pattama; Rakbud, Jittisak;

Abstract

Let X be a nonempty set, and let be a family of nonempty subsets of X with the properties that , and for all with . Let , and let . Then is a subsemigroup of the semigroup of functions on X having ranges contained in , where . For each , let be defined by . Next, we define two congruence relations and on as follows: and . We begin this paper by studying the regularity of the quotient semigroups and , and the semigroup . For each , we see that the equivalence class [] of under is a subsemigroup of if and only if is an idempotent element in the full transformation semigroup T(I). Let , and be the sets of functions in such that is injective, surjective and bijective respectively. We end this paper by investigating the regularity of the subsemigroups [], , and of .

Keywords

full transformation semigroup;regular element;character;

Language

English

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