Factor Congruence Lifting Property

TL;DR

This paper introduces and investigates the Factor Congruence Lifting Property in congruence-distributive algebras, exploring its relation to existing lifting properties and its implications in algebraic structures.

Contribution

It defines the new Factor Congruence Lifting Property and studies its properties and relationships with other lifting properties in algebraic contexts.

Findings

The property is related to the Congruence Boolean Lifting Property.

It provides insights into the structure of congruence-distributive algebras.

Connections with other lifting properties are established.

Abstract

In previous work, we have introduced and studied a lifting property in congruence--distributive universal algebras which we have defined based on the Boolean congruences of such algebras, and which we have called the Congruence Boolean Lifting Property. In a similar way, a lifting property based on factor congruences can be defined in congruence--distributive algebras; in this paper we introduce this property, which we have called the Factor Congruence Lifting Property, and study it, partly in relation to the Congruence Boolean Lifting Property, and to other lifting properties in particular classes of algebras.