Differential ring

From Citizendium
Revision as of 22:19, 20 December 2008 by Richard Pinch (Talk | contribs) (new entry, just a stub)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

In ring theory, a differential ring is a ring with added structure which generalises the concept of derivative.

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.