Document Type : Original Article
Department of Mathematics, University of Alabama, Tuscaloosa, AL 35487-0350, U.S.A.
Department of Mathematics, Research Institute of Natural Sciences, Hanyang University, Seoul 04763, Korea
Department of Mathematics, Payame Noor University, 19395-4697, Tehran, Iran
In this paper, we introduce the notion of a ringoid, and we obtain left distributive ringoids over a field which are not rings. We introduce several different types of ringoids, and also we discuss on (r, s)-ringoids. Moreover, we discuss geometric observations of the parallelism of vectors in several ringoids.