# Tagged Questions

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### A Version of Nullstellensatz for Rings of DÄ°fferential Operators

Here is one of the classical versions of the nullstellensatz: Let $K$ be a field and let $\mathfrak{m}$ be a maximal ideal of the polynomial ring $K[T_1,\ldots,T_n]$. Then ...
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### Cyclic vector theorem

Could be proved the cyclic vector theorem for a differential module (over a differential field of characteristic zero) by using the fact that the ring of differential operators (over the same ...
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### Does regularity of a D-module for an unusual filtration imply regularity for the usual one?

One definition of regular D-modules on affine space is that a D-module is regular if it has a filtration compatible with the order filtration on differential operators whose associated graded is ...
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### Idempotents in Rings of Differential Operators

Differential Operators on General Commutative Rings Let k be an algebraically closed field of characteristic zero, and let R be a commutative k-algebra. Then a (Grothendieck) differential operator ...
### What is the smallest $C^*$-algebra containing the “standard” pseudodifferential operators?
Is $\Psi^0(\mathbb{R})$ (pseudodifferential operators with symbols obeying $|\partial^\alpha_x \partial^\beta_\xi a(x,\xi)| \leq C_{\alpha,\beta} (1+|\xi|)^{-|\beta|}$ ) a $C^*$-algebra? In other ...
Let $\delta$ denote a non-zero complex algebraic differential operator in a single variable x. That is, it can be written as a sum $$\delta = \sum_i f_i\partial_x^i$$ where there $f_i$ are complex ...