# Difference between revisions of "Differential ring"

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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''. | 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''. | ||

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## Revision as of 21:45, 21 December 2008

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*.