On smallest (generalized) ideals and semilattices of (2,2)-regular non-associative ordered semigroups
Abstract
An ordered AG-groupoid can be referred to as a non-associative ordered semigroup, as the main di¤erence between an ordered semigroup and an ordered AG-groupoid is the switching of an associative law. In this paper, we dene the smallest left (right) ideals in an ordered AG-groupoid and use them to characterize a (2; 2)-regular class of a unitary ordered AG-groupoid along with its semilattices and (2 ;2 _q)-fuzzy left (right) ideals. We also give the concept of an ordered A*G**-groupoid and investigate its structural properties by using the generated ideals and (2 ;2 _q)-fuzzy left (right) ideals. These concepts will verify the existing characterizations and will help in achieving more generalized results in future works.
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