Formally, a differential ring is a ring R with an operation D on R which is a derivation:
- Every ring is a differential ring with the zero map as derivation.
- The formal derivative makes the polynomial ring R[X] over R a differential ring with
A differential ring homomorphism is a ring homomorphism f from differential ring (R,D) to (S,d) such that f·D = d·f. A differential ideal is an ideal I of R such that D(I) is contained in I.