On three generalizations of the group concept: groupoid, generalized group and almost groupoid

TL;DR

This paper explores three generalizations of groups—groupoid, generalized group, and almost groupoid—detailing their definitions, properties, and providing examples to illustrate their structures.

Contribution

It introduces and compares three new algebraic structures extending the concept of groups, with detailed definitions, properties, and examples.

Findings

Defined three generalized algebraic structures: groupoid, generalized group, almost groupoid

Presented constructions and examples of each structure

Compared properties and potential applications of these structures

Abstract

The aim of this paper is to describe the definitions and main properties of three generalizations of the group concept, namely: groupoid, generalized group and almost groupoid. Some constructions of these algebraic structures and corresponding examples are presented.