A homological approach to representations of algebras I: The wild case

We prove that the pure global dimension of a polynomial ring over an integral domain k in a finite or countable number n?2 of commuting (non-commuting, resp.) variables is t + 1, provided $\text{|k| = ?}{}_{\mathrm{t}}$. As an application, we determine the pure global dimension of wild algebras of quiver type, also (in case k is an algebraically closed field) of the wild local and wild commutative algebras of finite k-dimension.