Abstract
In this paper, we have given the generalized definition of an \(\mathcal{AG}\)-groupoid and defined a strongly regular \(\mathcal{AG}\)-groupoid as an \(\mathcal{AG}\)-groupoid in which every element has a left partial inverse with which it commutes. We have also proved that a strongly regular \(\mathcal{AG}\)-groupoid becomes right and left regular \(\mathcal{AG}\)-groupoids but the converses are not true in general. Further we have characterized the left, right, two-sided, interior, quasi and bi-ideals of a strongly regular \(\mathcal{AG}\)-groupoid and shown that all these ideals coincide in a strongly regular \(\mathcal{AG}\)-groupoid with left identity.
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