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Results tagged with ac.commutative-algebra
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user 161310
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
11
votes
Accepted
7
votes
0
answers
271
views
Is there a Swan-style description of topological K-homology?
A celebrated result of Swan [1] states that, on a compact Hausdorff space $X$, the category of finite rank complex vector bundles is equivalent to the category of finitely generated projective $\mathc …
- 1,020
7
votes
2
answers
808
views
Determining the kernel of the localization map when defining the localization by generators ...
All rings considered will be commutative and unitary. Let $A$ be a ring, $S \subseteq A$ a multiplicatively closed subset. The localization $\lambda_S : A \longrightarrow A[S^{-1}]$ can be characteriz …
- 7,893
2
votes
Determining the kernel of the localization map when defining the localization by generators ...
The proof of (LC3), in the given setting, is surprisingly difficult, or, at least, elaborate. Let $a \in A$ with $\lambda_S(a) = [a] = 0$ in $A[S^{-1}]$,
i.e. one has
\begin{equation}
\tag{1}
a \i …
- 1,020