On the Global Dimension of Incidence Algebras of Finite Lattices

Abstract We show that for any finite lattice $$\varvec{L}$$ L of order dimension $$\varvec{d}$$ d , the global dimension of its incidence algebra is at most $$\varvec{d}$$ 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.