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May
17
revised A proof for Atiyah-Macdonald Exercise I.21.iii
added 217 characters in body
May
17
comment A proof for Atiyah-Macdonald Exercise I.21.iii
@TakumiMurayama That is where my confusion lies. Maybe it is a shorthand for the set of all the elements in the contractions of the prime ideals containing $\mathfrak b$ (or a shorthand for the ideal generated by all these elements). The first equality in the last chain of equalities says $r (E^c) = r (E)^c$, which I only know to hold when $E$ is an ideal. I'm asking if there is a way to make sense of this "proof", because if the answer is yes, it is shorter than the other proof I found. But if the answer is no, then I will simply ignore it.
May
17
asked A proof for Atiyah-Macdonald Exercise I.21.iii
Apr
19
awarded  Taxonomist
Mar
3
accepted Solvable Lie algebra with codimension 1 ideal
Feb
5
comment First examples for topology of non-Hausdorff spaces
@EricWofsey What is an "inductive Mayer-Vietoris argument"?
Feb
5
comment First examples for topology of non-Hausdorff spaces
@PedroTamaroff The only broad thing about the question is the last paragraph, which is optional (should I say "bonus question"?).
Feb
5
asked First examples for topology of non-Hausdorff spaces
Dec
20
awarded  Constituent
Dec
8
awarded  Caucus
Sep
28
answered Calculus on Manifolds (Spivak), problem 2-41(a)
Sep
24
awarded  Autobiographer
Jul
22
comment Connection in fibre bundle from discontinuous group action
@Bombyxmori I think it is reasonable, considering that I "act in every direction". The formal argument I know invokes Poincaré duality to conclude: if a group $\Gamma$ acts (faithfully) on a contractible manifold $X$ and $\mathrm{cd} \, \Gamma = \dim X$, then $X / \Gamma$ is compact. ($\mathrm{cd}$ being the "cohomological dimension".)
Jul
22
revised Connection in fibre bundle from discontinuous group action
deleted 89 characters in body
Jul
2
awarded  Curious
Jun
22
awarded  Nice Question
Jun
17
awarded  Yearling
Jun
12
comment Number of Zeros of a Section vs Integral First Chern Class
Thanks. Any hint as to why this is true?
Jun
12
comment Number of Zeros of a Section vs Integral First Chern Class
"complex line bundles are actually classified by their first Chern class" Is this true for bundles over any base space?
May
18
reviewed Reviewed Solving of the first-order nonlinear differential equation