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
Famous quotes containing the words differential and/or ring:
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)
“I mount the steps and ring the bell, turning
Wearily, as one would turn to nod good-bye to Rochefoucauld,
If the street were time and he at the end of the street,
And I say, “Cousin Harriet, here is the Boston Evening Transcript.””
—T.S. (Thomas Stearns)