TL;DR
This paper proves that all finite bands (idempotent semigroups) have a finitely generated clone of term operations, resolving a long-standing open problem in algebra.
Contribution
It establishes that every finite band is finitely related, answering a question posed by Peter Mayr in 2013.
Findings
Finite bands are finitely related.
The clone of term operations is determined by finitely many relations.
Solves an open problem in algebra from 2013.
Abstract
We prove that every finite idempotent semigroup (band) is finitely related, which means that the clone of its term operations (i.e. operations induced by words) is determined by finitely many relations. This solves an open problem posed by Peter Mayr in 2013.
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