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Tagged with differential-algebra differential-operators
3 questions
8
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Semantics of derivations as derivatives
My understanding of how derivations on commutative rings are like derivatives is that a derivation on $R$ is differentiation with respect to a vector field on $\text{Spec}(R)$. But derivations are ...
7
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Differentially closed fields
Let F be a field. Recall that an additive map $d: F\rightarrow F$ is said to be a derivation if $d(ab)=ad(b)+d(a)b$.
Now let $F$ be a ring and let $d$ be a derivation of $F$. Examples I have in mind ...
1
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0
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Are all solutions to an ordinary differential equation continuous solutions to the associated implied differential equation and vice versa?
Now I have to heavily emphasize the fact that I have never studied differential algebra or the concept of other types of differentiation (which is what I believe is the concept behind a differential ...