On the Global Dimension of Incidence Algebras of Finite Lattices

Donghan Kim

doi:10.1007/s11083-026-09737-0

May 28, 2026OrderOpen Access

On the Global Dimension of Incidence Algebras of Finite Lattices

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Key Points

This work aims to determine the relationship between the order dimension of finite lattices and the global dimension of their incidence algebras.
Analysis of finite lattices of order dimension d.
Demonstration with a specific family of finite posets.
The global dimension of the incidence algebra is shown to be at most d.
An explicit family of finite posets illustrates that the inequality does not generally hold when not constrained to lattices.

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Implication

We show how global dimension relates to order dimension in finite lattices, suggesting limitations beyond this setting.

Abstract

We show that for any finite lattice L L of order dimension d d , the global dimension of its incidence algebra is at most d d . We also provide an explicit family of finite posets demonstrating that this inequality does not hold in general once the lattice assumption is removed.

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Cite This Study

Donghan Kim (2026) studied this question.

synapsesocial.com/papers/6a1a812b0307b785094330e7 https://doi.org/10.1007/s11083-026-09737-0

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On the Global Dimension of Incidence Algebras of Finite Lattices

Key Points

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Implication

Abstract

Discussion

Cite This Study

On the Global Dimension of Incidence Algebras of Finite Lattices

Key Points

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Implication

Abstract

Discussion

Cite This Study

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