Differential ring
From Knowino
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:
[edit] 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
[edit] Ideal
A differential ring homomorphism is a ring homomorphism f from a differential ring (R,D) to a differential ring (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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