On left distributive ringoids of groupoids

Year 2025, Volume: 74 Issue: 3, 411 - 423, 23.09.2025

Somayeh Borhani Nejad Rayeni , Akbar Rezaei

https://doi.org/10.31801/cfsuasmas.1575228

Abstract

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 $K.$

Keywords

Ringoid , quadratic-linear groupoid , linear-quadratic groupoid , quadratic-quadratic groupoid , left distributive ringoid

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