On the equational theory of finite modular lattices

2024/06/06 by Christian Herrmann, Herrmann, Christian
Computer Science · #03D40 #06B25 #06C05 #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2406.04237

openalex publication_date 2024/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• On the Finiteness Problem for classes of modular lattices
• On the consistency problem for modular lattices and related structures
• Engel-like Identities Characterizing Finite Solvable Groups
• On the complexity of equational decision problems for finite height(ortho)complemented modular lattices
• On some admissible lattices