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February 19, 2026Algebra UniversalisOpen Access

What is the weakest idempotent Maltsev condition that implies that abelian tolerances generate abelian congruences?

Keith A. Kearnes Emil W. Kiss

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Key Points

The research aims to identify the weakest idempotent Maltsev condition necessary for generating abelian congruences from abelian tolerances.
Analyzed properties of idempotent Maltsev conditions.
Examined implications for abelian tolerances.
Corrected errors found in a previous publication regarding congruence lattices.
Identified the minimal condition that suffices for the generation of abelian congruences.
Corrected foundational errors linked to the shape of congruence lattices.

Implication

Explores the minimal idempotent Maltsev condition enabling abelian tolerances to generate abelian congruences, correcting a previous error.

Abstract

We answer the question in the title. In the process, we correct an error in our AMS Memoir The Shape of Congruence Lattices .

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Cite This Study

Kearnes et al. (2026) studied this question.

synapsesocial.com/papers/69994c6f873532290d020eab https://doi.org/10.1007/s00012-026-00915-0

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