Independence concepts for groupoids

In this paper, for getting more results in groupoids, we consider a set and introduce the notion of a right (left) independent subset of a groupoid, and it is studied in detail. As a corollary of these properties, the following important result is proved: for any groupoid, there is a maximal right (left) independent subset.

Moreover, the notion of strongly right (left) independent subset is considered. It is proved that there exists a groupoid having a strongly right independent 2-set. Finally, we discuss the notion of dynamic elements with independence.