Non-associative semigroups in terms of semilattices via soft ideals

Algebraic structures play a prominent role in mathematics with wide ranging applications in many disciplines such as theoretical physics, computer sciences, control engineering, information sciences, coding theory, and topological spaces. This provides sufficient motivation to researchers to review various concepts and results from the realm of abstract algebra in the broader framework of fuzzy setting. In this paper, we introduce the notions of int-soft m , n -ideals, int-soft m , 0 -ideals, and int-soft 0 , n -ideals of semigroups by generalizing the concept of int-soft bi-ideals, int-soft right ideals, and int-soft left ideals in semigroups. In addition, some of the properties of int-soft m , n -ideal, int-soft m , 0 -ideal, and int-soft 0 , n -ideal are studied. Also, characterizations of various types of semigroups such as m , n -regular semigroups, m , 0 -regular semigroups, and 0 , n -regular semigroups in terms of their int-soft m , n -ideals, int-soft m , 0 -ideals, and int-soft 0 , n -ideals are provided.

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“…More concepts related to our study in different aspects have been studied in [33][34][35][36][37][38][39].…”

Section: Preliminariesmentioning

confidence: 99%

(m, n)-Ideals in Semigroups Based on Int-Soft Sets

Muhiuddin

Alanazi

2021

Journal of Mathematics

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“…Lemma 1 [29] For a nonempty subset A of an AG-groupoid S, the following conditions are equivalent: [29] Let S be an AG-groupoid. For ∅ = A, B ⊆ S, the following assertions hold:…”

Section: Basic Resultsmentioning

confidence: 99%

“…An AG-groupoid S is called an AG *** -groupoid [29] if the following conditions are satisfied: An AG-groupoid satisfying (i) is called an AG ** -groupoid. The condition (ii) for an AG ** -groupoid to become an AG *** -groupoid is equivalent to S = S 2 .…”

Section: Weakly Regular Ag *** -Groupoidsmentioning

confidence: 99%

A soft set theoretic approach to an AG-groupoid via ideal theory with applications

Yousafzai

Khalaf

2019

J Egypt Math Soc

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In this paper, we study the structural properties of a non-associative algebraic structure called an AG-groupoid by using soft set theory. We characterize a right regular class of an AG-groupoid in terms of soft intersection ideals and provide counter examples to discuss the converse part of various problems. We also characterize a weakly regular class of an AG***-groupoid by using generated ideals and soft intersection ideals. We investigate the relationship between SI-left-ideal, SI-right-ideal, SI-two-sided-ideal, and SI-interior-ideal of an AG-groupoid over a universe set by providing some practical examples.

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