Differential ring
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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.
References
- Andy R. Magid (1994). Lectures on Differential Galois Theory. AMS Bookstore, 1-2. ISBN 0-8218-7004-1.
- Bruno Poizat (2000). Model Theory. Springer Verlag, 71. ISBN 0-387-98655-3.