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Apr
26
revised What is the intuition behind a Euclidean function?
added 6 characters in body
Apr
26
comment Minimal free resolution of ideal generated by three homogeneous polynomials
@user26857: Yes, good point. Do you have a reference? I am looking but can't find any so far.
Apr
26
answered Minimal free resolution of ideal generated by three homogeneous polynomials
Apr
26
answered Do finite morphisms preserve dimensions?
Apr
24
comment Statement made by Borel on Linear Algebraic Groups page 79
Borel never claims that $K$ is a field extension of $k$, in fact you should rather think of $k$ as a field extension of $K$. Otherwise, the statement makes little sense.
Apr
23
comment Irreducible variety
Do you know that the image of a projective morphism is always closed?
Apr
20
comment A is an antisymmetric matrix (of even size). B is another matrix such that $b_{i,j}=a_{i,j}+c$. Prove that |A|=|B|
Eliminate all but the first $c$ in the first row by row operations, then eliminate all but the first $c$ in the first column by column operations and see what happens. If it's unclear, do this for a $4\times4$ example first. Next, use Laplace expansion for the first row and use the fact that the determinant of an odd-shaped antisymmetric matrix vanishes.
Apr
20
revised Graph theory: creating surfaces
edited tags
Apr
20
revised Isomorphism of Quotient ring $\Bbb Q[x]/\langle x^3\rangle$
added 51 characters in body; edited title
Apr
20
comment Why are there no $\mathbb{R}$-valued points on a complex curve?
I think I had a similar problem before. Maybe the answer there is helpful to you as well.
Apr
19
comment Localization Preserves Euclidean Domains
Me too actually. I knew the statement but had never thought about the proof before =).
Apr
19
revised Showing that the integers localized at a prime, p, is a Euclidean Domain
added 38 characters in body
Apr
19
comment Showing that the integers localized at a prime, p, is a Euclidean Domain
I answered this over here in more generality.
Apr
19
answered Localization of euclidean ring is euclidean?
Apr
19
revised Localization Preserves Euclidean Domains
added 19 characters in body
Apr
19
comment Localization Preserves Euclidean Domains
@rie: I changed the answer and corrected my mistake thanks to your insightful questions, indeed you have to make sure that $S$ is saturated for the argument to work.
Apr
19
revised Localization Preserves Euclidean Domains
added 1043 characters in body
Apr
18
comment Localization Preserves Euclidean Domains
No, my first statement refers to $N$, not $N_S$. Then I make some hyopthetical statements that are supposed to help you define $N_S$. After all, if any $N_S$ exists, then a multiplicative one exists as well. In fact, assuming $N$ multiplicative you can define $N_S$ which is multiplicative right away. You wanted a hint only. If you want the full solution, read the spoiler.
Apr
18
revised Localization Preserves Euclidean Domains
added 557 characters in body
Apr
18
answered Localization Preserves Euclidean Domains