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Results tagged with noncommutative-algebra
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user 2628
Non-commutative rings and algebras, non-associative algebras. Can be used in combination with ra.rings-and-algebras
8
votes
Accepted
Tensor products and two-sided faithful flatness
Here's an example. Let $R = {\mathbb C}[x]$ and let $S = {\mathbb C}\langle x,y\rangle/(xy-yx-1)$, i.e. the first Weyl algebra $A_1$. Then $S$ is free as both a left and right
$R$-module, and comes …
- 2,083
10
votes
Simplest examples of rings that are not isomorphic to their opposites
Hi Amri,
This is a bit late, but it's my favorite class of examples. If $X$ is a smooth affine variety over $\mathbb{C}$ (say), and $\mathcal{D} = \mathcal{D}(X)$ is its algebra of differential oper …
- 2,083
6
votes
Accepted
A Version of Nullstellensatz for Rings of Dİfferential Operators
I don't think it's true. Namely, Stafford showed ("Non-holonomic modules over Weyl algebras and enveloping algebras," Inventiones Mathematicae, 1985, Volume 79, Number 3, Pages 619-638) that if you c …
- 2,083