Characterizing the Ordered AG-Groupoids through the Properties of Their Different Classes of Ideals Реттелген AG-группоидтардың әртүрлi идеалды кластарының қасиеттерi бойынша сипаттамасы Характеризация упорядоченных AG-группоидов через свойства их различных классов идеалов

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KAUSAR N., Munir M., Gulzar M., Addis G.

Bulletin of the Karaganda University. Mathematics Series, vol.100, no.4, pp.101-112, 2020 (ESCI)

• Publication Type: Article / Article
• Volume: 100 Issue: 4
• Publication Date: 2020
• Doi Number: 10.31489/2020m4/101-112
• Journal Name: Bulletin of the Karaganda University. Mathematics Series
• Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
• Page Numbers: pp.101-112
• Keywords: left (right, interior, quasi-, bi-, generalized bi-) ideals, Ordered AG-groupoids, regular (intraregular) ordered AG-groupoids
• Open Archive Collection: AVESIS Open Access Collection
• Yıldız Technical University Affiliated: No

Abstract

In this article, we have presented some important charcterizations of the ordered non-associative semigroups in relation to their ideals. We have initially characterized the ordered AG-groupoid through the properties of the their ideals, then we characterized the two important classes of these AG-groupoids, namely the regular and intragregular non-associative AG-groupoids. Our aim is also to encourage the research and the maturity of the associative algebraic structures by studying a class of non-associative and non-commutative algebraic structures called the ordered AG-groupoid.