A differential ring is a ring R equipped with one or more derivations, that is additive homomorphisms
such that each derivation ∂ satisfies the Leibniz product rule
for every . Note that the ring could be noncommutative, so the somewhat standard d(xy) = xdy + ydx form of the product rule in commutative settings may be false. If is multiplication on the ring, the product rule is the identity
where means the function which maps a pair to the pair .
Read more about this topic: Differential Algebra
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