Characterizations of gamma-AG^{**}-groupoids by the properties their gamma-ideals
Madad Khan, Naveed Ahmad, Inayatur Rehman
TL;DR
This paper explores various ideal properties in gamma-AG^{**}-groupoids, establishing their structure and characterizations, especially in regular cases, and demonstrating that gamma-ideals form a semilattice.
Contribution
It introduces new characterizations of gamma-AG^{**}-groupoids based on their gamma-ideals and proves the semilattice structure of gamma-ideals in regular cases.
Findings
Gamma-ideals form a semilattice in regular gamma-AG^{**}-groupoids.
Regular gamma-AG^{**}-groupoids can be characterized via their left ideals.
Various types of gamma-ideals are discussed and characterized within gamma-AG^{**}-groupoids.
Abstract
In this paper we have discusses {\Gamma}-left, {\Gamma}-right, {\Gamma}-bi-, {\Gamma}-quasi-, {\Gamma}-interior and {\Gamma}-ideals in {\Gamma}-AG^{**}-groupoids and regular {\Gamma}-AG^{**}-groupoids. Moreover we have proved that the set of {\Gamma}-ideals in a regular {\Gamma}-AG^{**}-groupoid form a semilattice structure. Also we have characterized a regular {\Gamma}-AG^{**}-groupoid in terms of left ideals.
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Taxonomy
TopicsFuzzy and Soft Set Theory · Advanced Algebra and Logic · semigroups and automata theory