Jesko Hüttenhain
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 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 Apr 18 revised Hall subgroup property Markup / LaTeX fixed Apr 16 answered Blow-up and resolving a singularity Apr 16 comment Hypersurfaces have no embedded points (Vakil 5.5.I) It is of height one because it is principal and prime because it is the preimage of the prime ideal $P$. Apr 16 comment Understanding functions in $\mathbb{P}^1$ The divisor of this function is $[0:1]-[1:0]$, because it has a (single) zero at $[0:1]$ and a (single) pole at $[1:0]$, as you pointed out correctly. Apr 16 answered Hypersurfaces have no embedded points (Vakil 5.5.I) Apr 15 comment Intersection of hypersurfaces in the projective space This is true if you are thinking clasically, not scheme-theoretically. Let $\mathfrak m$ be the maximal ideal of your point $x$ and let $\mathfrak m^k = (f_1,\ldots,f_m)$. The $f_i$ are homogeneous of degree $k$ and each of them defines a hypersurface $Z_i$. Then, $Z_1\cap\cdots\cap Z_m=Z(f_1,\ldots,f_m)=Z(\mathfrak m^k)=Z(\mathfrak m)=\{x\}$. Apr 14 comment Maximum matchings in a bipartite graph But you said "$S$ is a set of vertices $S\subset X$". Apr 14 comment Maximum matchings in a bipartite graph This is precisely the Hall condition. Apr 13 comment the intersection of an empty family of sets; what's wrong with this proof? Your mistake is when you say "then $x\in A$ for some $A\in S$". There is no such $A$ if $S=\emptyset$. In fact, when $S$ is the empty set, then $\forall A\in S\colon x\in A$ is true for every set $x$. A good way to check for mistakes is by going through your proof and substituting $S$ for $\emptyset$ all the time and see what happens. Apr 13 comment Normal closure of $\mathbb{Q}(\sqrt{11+3\sqrt{13}})$ over $\mathbb{Q}$ To be frank, I used a computer algebra system simply to confirm my suspicion. But the general method is outlined on wikipedia. It's a bit tricky. Apr 13 answered Normal closure of $\mathbb{Q}(\sqrt{11+3\sqrt{13}})$ over $\mathbb{Q}$ Apr 13 answered Morphism whose fibers are finite and reduced is unramified Apr 13 revised Prove that the determinant of an invertible matrix $A$ is equal to $±1$ when all of the entries of $A$ and $A^{−1}$ are integers. LaTeX Apr 13 answered Prove that the determinant of an invertible matrix $A$ is equal to $±1$ when all of the entries of $A$ and $A^{−1}$ are integers. Apr 12 revised Finding the Dimension of a given space V added 13 characters in body Apr 12 revised Finding the Dimension of a given space V added 453 characters in body Apr 12 answered Finding the Dimension of a given space V