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Results tagged with ra.rings-and-algebras
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user 2628
Non-commutative rings and algebras, non-associative algebras, universal algebra and lattice theory, linear algebra, semigroups. For questions specific to commutative algebra (that is, rings that are assumed both associative and commutative), rather use the tag ac.commutative-algebra.
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