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seen Feb 5 at 1:43

Oct
7
awarded  Scholar
Oct
7
accepted Why is this ring not Cohen-Macaulay?
Oct
7
comment Why is this ring not Cohen-Macaulay?
Ah, thanks! This is the right question to ask and which I couldn't come up with! In $k[x,y]$ we have $(x^3y)^2=x^4(x^2y^2)$. Since $k[x,y]$ is an integral domain, hence cancellative as a multiplicative monoid, $x^2y^2$ is the only element we can multiply with $x^4$ to get $(x^3y)^2$. Hence it is enough to show that $x^2y^2$ is not in the subring $R$. But this is true because no monomial in $R$ has degree in $x$ and in $y$ both smaller than $3$.
Oct
7
revised Why is this ring not Cohen-Macaulay?
added a clarification
Oct
7
asked Why is this ring not Cohen-Macaulay?
Sep
6
awarded  Promoter
Aug
30
revised Is it true in a presentable infinity category that algebras are homotopy colimits of free algebras?
added 36 characters in body
Aug
30
comment Is it true in a presentable infinity category that algebras are homotopy colimits of free algebras?
Oh sorry, I didn't note how this could be misunderstood. I wanted to know about an $\infty$-categorical version of the 1-categorical statement. I clarified the question accordingly...
Aug
30
revised Is it true in a presentable infinity category that algebras are homotopy colimits of free algebras?
added 39 characters in body
Aug
29
awarded  Student
Aug
29
asked Is it true in a presentable infinity category that algebras are homotopy colimits of free algebras?
Aug
28
awarded  Necromancer
Sep
30
comment What structure does the alternating group preserve?
I don't know whether the construction of the Tits building is functorial. I didn't mean to imply this with anything I wrote. It would be nice of course, then an embedding of S_n might correspond to the inclusion of a particular chamber.
Sep
29
revised What structure does the alternating group preserve?
added link
Sep
29
comment What structure does the alternating group preserve?
I am also starting to find that strange now: Does an embedding of S_n into GL_n give me a choice of basis? Maybe via picking eigenvectors? If not one could define A_n as the intersection of S_n with O_n (which is definable coordinate-free) under any embedding - and then use coordinates to show independence of the embedding.
Sep
29
comment What structure does the alternating group preserve?
Does it? Aren't the group operations still there when you forget about the coordinates, which you used to define it via matrix multiplication? The construction of the building then uses just coordinate-free notions like "Borel subgroups", as far as I remember...
Sep
28
answered What structure does the alternating group preserve?
Sep
27
comment Best book ever on Number Theory
works fine when I try
Sep
26
answered Best book ever on Number Theory
Sep
25
revised geometric meaning of differentiation with respect to the complex conjugate of $z$
added 55 characters in body