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Results tagged with division-rings
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user 22989
A division ring is a possibly noncommutative ring where every nonzero element has a two-sided multiplicative inverse.
12
votes
Accepted
Infinite dimensional finitely generated algebraic division algebra
This is a fairly well known old and open (as far as I know) problem: Kurosh’s Problem for division rings. See, for example, Question 3 in Agata Smoktunowicz’s 2006 ICM talk.
- 35.2k
7
votes
Accepted
Dimension of division rings coming from indecomposable modules
Even if $A$ is a finite dimensional $k$-algebra, there may be no bound on the dimension of $\text{End}_A(X)/m$.
Let $Q$ be the Kronecker quiver (i.e., the quiver with two vertices and two arrows from …
- 35.2k
4
votes
Accepted
Extending an automorphism to an inner one
For Q1, you can form the skew polynomial ring $D[t;f]$ (i.e., the ring of polynomials in $t$ with coefficients from $D$, and multiplication satisfying $tr=f(r)t$ for $r\in D$). This is an Ore domain, …
- 35.2k