Coextensive varieties via Central Elements

TL;DR

This paper characterizes coextensive varieties using central elements, showing that under certain conditions, coextensivity is equivalent to being a variety of shells.

Contribution

It introduces a new characterization of coextensive varieties via central elements, especially for finite type, congruence-permutable varieties with universal indecomposables.

Findings

Coextensivity is characterized by being a variety of shells under specified conditions.

Central elements provide a key tool for understanding coextensive varieties.

The paper links coextensivity with structural properties like congruence-permutability and universality.

Abstract

In this paper we use the theory of central elements in order to provide a characterization for coextensive varieties. In particular, if the variety is of finite type, congruence-permutable and its class of directly indecomposable members is universal, then coextensivity is equivalent to be a variety of shells.