Generalized ring-groupoids

Abstract

In this work, we are going to present the concept of generalized ring-groupoid.
Also, we are going to investigate some characterizations about the generalized ring-groupoids. We are going to introduce the concept of generalized subring-groupoid. So we construct the category of generalized ring-groupoids. Furthermore, we are going to discuss a new class of the generalized ring-groupoids, which we will say it ”M-ring-groupoid”. In the end of the paper, we are going to give the product of generalized ring-groupoids.