On left distributive ringoids of groupoids

In this paper, we investigate and study some types of left distributive ringoids over a field which are not rings. For this, we first introduce (quadratic-linear, linear-quadratic, quadratic-quadratic) groupoids over a field, then find their general form, and in the following left distributive ringoids are investigated with respect to these groupoids. Finally, we find the general form of the left distributive quadratic-linear, linear-quadratic, and quadratic-quadratic ringoids over a field $K.$