Some General Properties of Stein AG-groupoids and Stein AG-Test

A groupoid S that satisfies the left invertive law: ab . c = cb . a is called an AG-groupoid. We extend this concept to introduce a Stein AG-groupoid. We prove the existence of this type of AG-groupoid by providing some non-associative examples. We also explore some basic and general properties of these AG-groupoids and find their relations with other known subclasses of AG-groupoids. We present a table of enumeration for these AG-groupoids up to order 6 and further categorize into associative and non-associative. We also develop a method to test an arbitrary AG-groupoid for this new class. Further, we also characterize these AG-groupoids by the properties of their ideals.