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<p>It is shown that there is <i>N</i> such that there is no algorithm to decide for identities in at most <i>N</i> variables validity in the class of finite modular lattices. This is based on Slobodskoi’s result that the Restricted Word Problem is unsolvable for the class of finite groups and relies on Freese’s technique of capturing group presentations within free modular lattices.</p>

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On the Equational Theory of Finite Modular Lattices

  • 期刊论文

  • 发表日期：

    2025年9月9日

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  • Christian Herrmann

摘要

It is shown that there is N such that there is no algorithm to decide for identities in at most N variables validity in the class of finite modular lattices. This is based on Slobodskoi’s result that the Restricted Word Problem is unsolvable for the class of finite groups and relies on Freese’s technique of capturing group presentations within free modular lattices.