## New answers tagged homological-algebra

3
votes

Accepted

### When is the Tor-dimension of $R/(r)$ strictly smaller than that of $R$?

There is no difference between flat (Tor) dimension and global dimension for Noetherian rings. Now, it is well known that for an arbitrary local $R$ and a nonzerodivisor $f\in\mathfrak{m}$ either $\...

8
votes

Accepted

### Morita equivalences and centers of some algebras

The answer is that in your matrix $\left(\begin{smallmatrix} 0&x_0\\0&0\end{smallmatrix}\right)$, the $x_0$ denotes the isomorphism of modules given by left multiplication by $x_0$, so it ...

22
votes

Accepted

### Who wrote `if only I could understand the equation $d^2=0$'?

Here’s a synthesis of answers and comments by მამუკა ჯიბლაძე and Georges Elencwajg fleshed out by your obedient servant.
On June 25, 1980, Henri Cartan was admitted to the honorary degree of Doctor of ...

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