A structure theorem for differential algebras
Marcus Tressl · Banach Center Publications · 2002
Theorem 1. Let S = (S, ∂1, ..., ∂K) be a differential domain in K commuting derivatives, containing Z and let R = (R, ∂1, ..., ∂K) ⊆ (S, ∂1, ..., ∂K) be a differential subring such that S is differentially finitely generated over R. Then there are R-subalgebras B and P of S and an element h ∈ B, h 6= 0 such that: (a) B is a finitely generated R-algebra and Bh is a finitely presented R-algebra. (b) Sh = (B ·P )h is a differentially finitely presented R-algebra. (c) The homomorphism B⊗R P −→ B·P induced from multiplication is an isomorphism of R-algebras.