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Abstract <p>We prove that the class of subdirectly irreducible acts over a fixed finite semigroup is finitely axiomatized. We establish that the class of subdirectly irreducible acts over an infinite right (left) zero semigroup and over an infinite elementary Abelian 2-group is not finitely axiomatized.</p>

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Axiomatization of Some Classes of Acts over Semigroups

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • D. S. Khramchenok

摘要

Abstract

We prove that the class of subdirectly irreducible acts over a fixed finite semigroup is finitely axiomatized. We establish that the class of subdirectly irreducible acts over an infinite right (left) zero semigroup and over an infinite elementary Abelian 2-group is not finitely axiomatized.