Fundamental relations in multialgebras. Applications

TL;DR

This paper characterizes fundamental relations in multialgebras using poset properties of equivalence relations, and demonstrates applications including hyperring commutativity and categorical properties of fundamental algebra constructions.

Contribution

It introduces a new characterization of fundamental relations in multialgebras and applies it to hyperrings and categorical algebra constructions.

Findings

New characterization of fundamental relations in multialgebras

Application to hyperring commutativity

Category-theoretic properties of fundamental algebra construction

Abstract

Based on the properties of the poset of those equivalence relations of a multialgebra for which the factor multialgebra is a universal algebra, we give a characterization for the fundamental relations of a multialgebra. We point out the benefits of our approach by giving two applications. One of them provides a new characterization of the commutative fundamental relation of a hyperring, and the other will give a general category theoretical property of the construction of the fundamental algebras (both in the general case and in the hyperring case).