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1
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0answers
147 views

Separability and smoothness

Let $A \subseteq B$ be commutative noetherian rings. I have found the following claim: "Separability implies smoothness" with the following explanation: "The natural thing is to prove that a separable ...
-3
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0answers
99 views

Non-flat $R \subseteq S$, which is integral, separable, $R$ is a noetherian (not integrally closed) integral domain

On ramification theory in noetherian rings, of Auslander and Buchsbaum say: "Chapter 4 is devoted to showing that under various conditions if $S$ is unramified over $R$, then $S$ is $R$-projective. ...
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0answers
54 views

Are the fibers of this morphism geometrically regular?

Let $A\rightarrow B$ be a local morphism of complete noetherian rings making $B$ a formally smooth $A$-algebra. Does the induced morphism $\textrm{Spec}(B)\to\textrm{Spec}(A)$ have geometrically ...
8
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1answer
183 views

Is every separable algebra in a modular tensor category Morita equivalent to a commutative one?

Separable algebras in modular tensor categories are interesting algebraic structures, which have received significant attention because of their connection to conformal field theories. My ...
0
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0answers
231 views

Finite separable extension of fields imply the number of intermediate subfield is finite

The proof of statements either uses Galois theory or Artin primitive element theorem.I would like to know whether there is a proof without using these.The reason to avoid using Galois theory is that ...
7
votes
0answers
211 views

Non Commutative Hyperspaces

Let $X$ be a compact metric space. Recall that the hyperspace $2^{X}$ is the set of all non empty compact subsets of $X$ with the Hausdorff metric. Assume that $\mathcal{C}$ is the category of all ...
3
votes
2answers
366 views

An R-algebra A is R-separable if and only if all derivations are inner.

Hello everybody. I'm readying about derivations. It is very very known fact that all derivations $\delta: A\rightarrow M$ (A R-algebra, M A-module) are inner when the algebra is R-separable. ...
2
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1answer
328 views

On the Separability of Certain Extensions of Fields.

Hi, I made this question a couple of weeks ago. The question arose while looking for a criterion of separability for extensions of fraction fields $K(A)\to K(B)$ induced by a faithfully flat ...
7
votes
1answer
277 views

Hochschild H^1 (R,M) = 0 vs. H_1 (R,M) = 0 where R is a ring and M is an (R,R)-bimodule

Let $k$ be a commutative ring (with unity). Let $R$ be a $k$-algebra (with unity, but not of necessity commutative). Let $M$ be an $\left(R,R\right)$-bimodule where $k$ acts in the same way from the ...