# Tag Info

## Hot answers tagged noncommutative-algebra

### What do you do if you believe a problem is undecidable?

The first thing to say is that for a statement to be independent of some axioms means really two things, namely, that it is consistent with those axioms, and also that the negation of the statement is ...

• 49.4k

Accepted

### RIng that is flat over a subring as a right module but not as a left module

Take the associative algebra over a field $k$, with generators $x$ and $y$ subject to the relation $xy=0$. This admits a basis consisting of monomials of the form $y^a x^b$. It thus contains a subring ...
• 6,049

### What properties "should" spectrum of noncommutative ring have?

I know this question is old, and has an accepted answer, but this excellent paper by Manny Reyes gives some further thoughts about possible Spec's for noncommutative rings.
• 14.9k
If $X$ is smooth projective and $D = \cup D_i \subset X$ is an ample divisor so that $Y = X \setminus D$ is affine, then there is an exact sequence  \oplus {\mathbb Z}D_i \to Pic X \to Pic Y \to 0. \$...