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visits member for 1 year, 11 months
seen 5 hours ago

I guess I'm a graduate student now. That's a little weird.

This will remain the account that I use to anonymously ask stupid questions.


5h
comment Number of elements of a prime ideal's coset
It is a field. What is the inverse of 1? It is helpful to know that an ideal $I$ of a commutative ring $R$ is maximal iff $R / I$ is a field.
9h
answered Number of elements of a prime ideal's coset
1d
comment Is there are “sphere” associated to any topological vector space?
@Jochen But that is the $n-1$ sphere in the $R^n$ case, so the "dimension" is not what I wanted. Thanks though...
Nov
24
comment Is there are “sphere” associated to any topological vector space?
Being precise about sphere like objects is somewhat simple: a construction that gives $S^n$ from $R^n$ for all $n$, and that can also be applied to a TVS.
Nov
24
comment Is there are “sphere” associated to any topological vector space?
@k.stm My response was also a joke. I'm glad that we are on the same page now. :)
Nov
24
comment Is there are “sphere” associated to any topological vector space?
@k.stm If a question can be answered with "no," then it is not vague, since it can be interpreted decisively.
Nov
24
asked Is there are “sphere” associated to any topological vector space?
Oct
26
accepted Geometric meaning of intersection multiplicities?
Oct
25
asked Geometric meaning of intersection multiplicities?
Oct
25
asked Elimination theory in Hartshorne
Oct
14
accepted Over an algebraically closed field, is it possible to factor a symmetric invertible matrix $A$ as $X^T X$?
Oct
14
asked When is $A = k[x_1,\ldots, x_n]/I$ integrally closed?
Oct
9
comment Over an algebraically closed field, is it possible to factor a symmetric invertible matrix $A$ as $X^T X$?
@Omnomnomnom This is used in the complex case on page 58 of Miranda's Riemann Surfaces and Algebraic Curves in order to prove that the smooth conics in $P^2$ are isomorphic to $P^1$. I want to prove this for conics in $P^2$ for some arbitrary (algebraically closed) field, so it was natural to ask about this extension. So for my purposes it would really need to be the transpose.
Oct
9
revised Over an algebraically closed field, is it possible to factor a symmetric invertible matrix $A$ as $X^T X$?
edited title
Oct
9
comment Over an algebraically closed field, is it possible to factor a symmetric invertible matrix $A$ as $X^T X$?
@Omnomnomnom I'm pretty sure that it's just the transpose, since one only specifies that the original matrix $A$ is symmetric.
Oct
9
asked Over an algebraically closed field, is it possible to factor a symmetric invertible matrix $A$ as $X^T X$?
Oct
5
comment Tensoring $k[x] \otimes_k k[y]$
I think another way to see that it is an injection is to check that the induced map is a homomorphism of graded $k$ algebras, and since each of the degree $d$ homogeneous submodules is a finite dimensional vector space, surjectivity there implies injectivity. Is there some slick way to see that the tensor product over $k$ is the coproduct in the category of commutative $k$-algebras?
Oct
5
accepted Tensoring $k[x] \otimes_k k[y]$
Oct
5
comment Tensoring $k[x] \otimes_k k[y]$
@mt_ haha, oh goodness. thanks.
Oct
5
asked Tensoring $k[x] \otimes_k k[y]$