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Abstract <p>We prove that some quotient algebra of any binary idempotent algebra with an associative hyperidentity is a semilattice. It is well-known that every idempotent semigroup is locally finite. We give a general version of this result concerning to idempotent algebras with an associative hyperidentity. As a consequence we obtain new idempotent Burnside varieties of binary algebras in which every finitely generated algebra is finite.</p>

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On the Structure of Idempotent Algebras with an Associative Hyperidentity. Burnside Varieties

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Yu. Movsisyan

摘要

Abstract

We prove that some quotient algebra of any binary idempotent algebra with an associative hyperidentity is a semilattice. It is well-known that every idempotent semigroup is locally finite. We give a general version of this result concerning to idempotent algebras with an associative hyperidentity. As a consequence we obtain new idempotent Burnside varieties of binary algebras in which every finitely generated algebra is finite.