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Results tagged with ac.commutative-algebra
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user 94086
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
7
votes
1
answer
268
views
Geometric object corresponding to subalgebra generated by an ideal?
This question is closely related to What is the geometric object corresponding to a subalgebra in a polynomial ring.
There, it is asked, given a subalgebra of an algebra $S \subset R$ over a field $k$ …
- 1,142
3
votes
0
answers
251
views
Cohen structure theorem with explicit equations
By Cohen structure theorem, a complete regular equicharacteristic Noetherian local ring is isomorphic to a power series. In particular, this should hold for finite extensions of power series $k[[t]][\ …
- 1,142
7
votes
1
answer
826
views
Intersection of free/affine submodules, comparison with vector spaces
If $W_1,W_2 \subset V$ are finite-dimensional $k$-vector spaces of dimensions $d_1, d_2 \leq d$, respectively, then $d_1 + d_2 > d$ suffices to guarantee $W_1 \cap W_2 \neq \{0\}$. There are similar r …
- 1,142
7
votes
2
answers
322
views
How to understand the "boundary" of subscheme, as defined in "An elementary characterisation...
In An elementary characterisation of Krull dimension and A short proof for the Krull dimension of a polynomial ring, Coquand, Lombardi, and Roy give an elementary characterization of Krull dimension, …
- 1,142