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Jan
22
answered Let $f: U \rightarrow W$ be a morphism of affine algebraic sets and $f': k[W] \rightarrow k[U]$ be the k-algebra morphism of coordinate rings.
Jan
5
answered If $xa=xb$ then $a=b$
Dec
24
revised Maximal solvable subgroup not Borel
edited tags
Dec
21
awarded  Constituent
Dec
11
answered quotient is a projective variety
Dec
8
awarded  Caucus
Dec
6
revised Invariants of $O(2) \times O(2)$ under simultaneous conjugation
added 1788 characters in body
Dec
5
answered Invariants of $O(2) \times O(2)$ under simultaneous conjugation
Dec
4
revised action of $GL_3$ on $P^2$
added 128 characters in body
Dec
4
answered action of $GL_3$ on $P^2$
Dec
4
revised action of $GL_3$ on $P^2$
edited tags
Dec
4
comment Order of product of abelian group
I think you have only shown that the order of $c=ab$ divides $\operatorname{lcm}(m,n)$. This does not prove that they are equal.
Dec
4
comment Order of product of abelian group
No, this is not true. from $b^n=a^{-m}$ you can not conclude $b^{n-1}=a^{-(m-1)}$ because $a^{-(m-1)}=a^{-m+1}=b^{n+1}\ne b^{n-1}$ in general. I have a feeling the order should be the least common multiple of $m$ and $n$.
Dec
3
comment How does Molien series describe polynomial invariants?
@monomorphic: You got it. Unfortunately, I am afraid I have never seen a proof of Molien's theorem and you might best be served asking this as another question, I am sure someone here can help you with that.
Dec
3
comment How does Molien series describe polynomial invariants?
@monomorphic: Alright =)
Dec
3
comment How does Molien series describe polynomial invariants?
@monomorphic: The Molien series does not really describe the polynomial invariants. I do not think it is possible to reconstruct the polynomial invariants from the Molien series. The Molien series is really just a power series whose $d$-th coefficient is the number of linearly independent polynomial invariants of degree $d$. What uniqueness are you referring to?
Dec
3
comment How to prove that $Aut(\mathbb{P}^2) \cong PSL_3 (\mathbb{C})$?
Sure thing. I left an answer for you, maybe it can help.
Dec
3
answered How does Molien series describe polynomial invariants?
Dec
3
comment How to prove that $Aut(\mathbb{P}^2) \cong PSL_3 (\mathbb{C})$?
This fact (or actually, a more general statement) is known as the "Fundamental Theorem of Projective Geometry". You can find it as Theorem 1.5 in this book, which is available online. What you are looking for is the Corollary 1.7.
Dec
3
answered Finding Basis for a Radical of an Ideal