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<p>Two problems are well known in universal algebra and lattice theory: which finite lattices have a finite basis for their quasiidentities, and which finite lattices generate standard topological quasivarieties? This paper presents sufficient conditions under which a locally finite quasivariety of lattices is non finitely axiomatizable and nonstandard. As a consequence, we provide a wider class of varieties of modular lattices in which every proper finitely generated subquasivariety is not finitely axiomatizable and nonstandard.</p>

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Non Finitely Axiomatizable and Nonstandard Quasivarieties of Modular Lattices

  • 期刊论文

  • 发表日期：

    2026年7月11日

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  • M. A. Arapbay,
  • A. M. Asanbekov,
  • A. O. Basheyeva,
  • A. M. Nurakunov

摘要

Two problems are well known in universal algebra and lattice theory: which finite lattices have a finite basis for their quasiidentities, and which finite lattices generate standard topological quasivarieties? This paper presents sufficient conditions under which a locally finite quasivariety of lattices is non finitely axiomatizable and nonstandard. As a consequence, we provide a wider class of varieties of modular lattices in which every proper finitely generated subquasivariety is not finitely axiomatizable and nonstandard.