An -groupoid can be referred to as a non-associative semigroup, as the main difference between a semigroup and an -groupoid is the switching of an associative law. In this paper, we define the smallest one-sided ideals in an -groupoid and use them to characterize a strongly regular class of a unitary -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 -groupoid and give an example to show that this class is the generalization of a unitary -groupoid.
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