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Results tagged with ac.commutative-algebra
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user 468
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
38
votes
Accepted
Do there exist non-PIDs in which every countably generated ideal is principal?
No such ring exists.
Suppose otherwise. Let $I$ be a non-principal ideal, generated by a collection of elements $f_\alpha$ indexed by the set of ordinals $\alpha<\gamma$ for some $\gamma$. Consid …
- 6,327
1
vote
Accepted
Representation dimension of a special algebra
I don't think (*) is correctly copied from the paper. The corresponding claim in the paper is that every morphism from an indecomposable summand of $M$ except for the identity morphism from $T$ to $T …
- 6,327
12
votes
2
answers
323
views
Easy way to understand theta basis for X-cluster algebras of finite type?
For $\mathcal A$-cluster algebras of finite type, it is very easy to describe the theta-basis: it consists of the cluster monomials. Is there any similarly easy way to describe the theta-basis for $\m …
- 6,327
6
votes
Nonfree projective module over a regular UFD?
What about $R = \mathbb R[x,y,z]/\langle x^2+y^2+z^2-1\rangle$ and $M$ the projective module corresponding to the tangent bundle? This seems to satisfy your criteria except probably for factorialness …
- 6,327
12
votes
1
answer
1k
views
What is a good introduction to cluster algebras from surfaces?
What is a good reference for cluster algebras from surfaces, with a view to their connection to Teichmuller theory?
In my view, that means it should start off with unpunctured surfaces (and in fact …
- 6,327