Green s relations, ideals and regularity on semigroups of partial transformations with invariant set

Name: Jitsupa Srisawat

keyword: Partial transformation semigroups

; Green's relations Ideals

; Unit-regular semigroups

; Coregular semigroups

; Directly finite semigroups

Abstract: Let X be a nonempty set. A partial transformation semigroup is the set of all functions from a subset of X into X under the composition of functions, denoted by P(X). For a fixed proper subset Y of X, let PFix(X,Y)={\alpha\in P(X) : y\alpha=y for all y\in\dom\alpha\cap Y}. For \emptyset\neq Y\subseteq X, let \pt=\{\alpha\in P(X) : (\dom\alpha\cap Y)\alpha\subseteq Y\}. Then PFix(X,Y) and \pt are subsemigroups of P(X) and PFix(X,Y)\subseteq\pt. Since \overline{PT}(X,X)=P(X) and PFix(X,\emptyset)=P(X), both semigroups are regarded as extensions of $P(X)$. This thesis explores several well-known and crucial concepts in semigroup theory, including Green's relations, unit-regularity and coregularity in the semigroup \pt. Additionally, we delve into the study of directly finiteness and ideals in both \pt and PFix(X,Y).

Thammasat University. Thammasat University Library

Address: BANGKOK

Email: preserv@tu.ac.th

Name: Yanisa Chaiya

Role: advisor

Created: 2024

Modified: 2024-10-24

Issued: 2024-10-24

วิทยานิพนธ์/Thesis

application/pdf

DOI: 10.14457/TU.the.2023.375

eng

DegreeName: Master of Science

Level: Master's Degree

Descipline: Mathematics

Grantor: Thammasat University

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