Diagram of Representations of Universal Algebras

TL;DR

This paper explores the theory of representations of universal algebras, focusing on diagrams, morphisms, and foundational concepts like generating sets and bases, advancing the structural understanding of these representations.

Contribution

It introduces the concept of diagrams of representations and examines morphisms, generating sets, and bases, providing a structured framework for universal algebra representations.

Findings

Defined morphisms that preserve representation structure

Explored the concepts of generating sets and bases

Developed a diagrammatic approach to representations

Abstract

Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism of the representation is the map that conserve the structure of the representation. Exploring of morphisms of the representation leads to the concepts of generating set and basis of representation.