Differential ring

From Citizendium
Revision as of 16:31, 12 June 2009 by Jitse Niesen (Talk | contribs) (use \cdot for multiplication)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search
This article is a stub and thus not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

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:

Examples

  • 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

Ideal

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.