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Results tagged with dimension-theory
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user 5292
Hausdorff dimension, box dimension, packing dimension and similar concepts.
30
votes
1
answer
13k
views
Rank of a module
What's wrong with defining the rank of a finitely generated module over any (commutative) ring to be just the smallest number of generators? All books I know define rank only locally this way. But why …
- 2,857
5
votes
1
answer
4k
views
Dimension of module
Does dimension of a module (say, dimension of its support) have anything to do with the supremum length of chains of prime submodules like rings?
Let's restrict to finitely generated modules over Noet …
- 2,857
4
votes
2
answers
770
views
Converse of Principal Ideal Theorem
$(A, \mathfrak{m})$ a Noetherian local ring, $a\in\mathfrak{m}$ a zero divisor. Then is it true that $\mbox{dim}\ A/(a) = \mbox{dim}\ A$ ?
- 2,857
0
votes
1
answer
2k
views
Dimension of tensor product of modules
$A\rightarrow B$ a ring homomorphism of Noetherian rings, where $A$ is local. $M$, $N$ finitely generated and nonzero $A$- and $B$- modules, respectively. Then I seem to get $\mbox{dim}_ {B}(M\otimes …
- 2,857