Isotopic algebras with non-isomorphic congruence lattices

TL;DR

This paper provides examples of isotopic algebras that have non-isomorphic congruence lattices, demonstrating that isotopy does not necessarily imply isomorphism of congruence structures.

Contribution

It answers an open question by showing that isotopic algebras can have different congruence lattices, challenging assumptions about their structural similarities.

Findings

Examples of isotopic algebras with non-isomorphic congruence lattices

Disproof of the conjecture that isotopic algebras always have isomorphic congruence lattices

Clarification of the relationship between isotopy and congruence lattice isomorphism

Abstract

We give examples of pairs of isotopic algebras with non-isomorphic congruence lattices. This answers the question of whether all isotopic algebras have isomorphic congruence lattices.