Non-associative semigroups in terms of semilattices via soft ideals

Article type: Research Article

Authors: Yousafzai, Faisal^{a; *} | Ali, Arshad^a | Haq, Shamsul^b | Hila, Kostaq^c

Correspondence: [*] Corresponding author. Faisal Yousafzai, Military College of Engineering, National University of Sciences and Technology (NUST), Islamabad, Pakistan. E-mail: [email protected].

Abstract: An AG -groupoid can be referred to as a non-associative semigroup, as the main difference between a semigroup and an AG -groupoid is the switching of an associative law. In this paper, we define the smallest one-sided ideals in an AG -groupoid and use them to characterize a strongly regular class of a unitary AG -groupoid along with its semilattices and SI-l-ideals (SI-r-ideals) and SI-bi-ideals. As an application, we get some interesting and new characterizations which we usually do not find in semigroups. Finally we give the concept of an AG*** -groupoid and give an example to show that this class is the generalization of a unitary AG -groupoid.

Keywords: S-sets, pseudo-inverses, AG^***-groupoid, left invertive law, smallest one-side (soft) ideals

DOI: 10.3233/JIFS-18873

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 4, pp. 4837-4847, 2018