Rezaei, AkbarKim, Hee SikBorzooei, Rajab AliSaeid, Arsham Borumand2024-05-192024-05-1920230354-5180https://doi.org10.2298/FIL2330275Rhttps://hdl.handle.net/20.500.12713/5311We will study the notion of right distributive ringoids over a field which are neither rings, semi-rings, semi-hyperrings nor near-rings. Matrices over ringoids are defined, and new concepts such as top-row-determinate and down-row-determinate related to 2 x 2 matrices over a ringoid are introduced. Moreover, we investigate the notions of the (strongly, (very-) weak) orthogonality of vectors over a ringoid. Beside, we discuss the notion of incident vectors and define the concept of alpha -K-sphere on a ringoid, where K is a field and investigate some of their properties. Finally, we show that in a commutative ringoid all of the vectors are strongly orthogonal.eninfo:eu-repo/semantics/closedAccessLeft Zero(Right-) Distributive) Ringoid(Linear) Groupoid(Strongly(Very-) Weak) OrthogonalArticle37301027510288WOS:001097473700001N/A10.2298/FIL2330275R