I'll define the Verlinde category, which is a novel tensor category in characteristic p > 0 whose objects cannot be realized as vector spaces in a precise sense. One can still make sense of commutative rings in the Verlinde category, with the added challenge that one cannot really talk about elements in the ring. We will see that, like in the category of vector spaces, the Hilbert's basis theorem holds, i.e., finitely generated algebras are noetherian, a result due to Venkatesh.