Graduate student mostly dabbling in algebraic geometry.

18h
answered Galois Group for $x^5-1$
18h
comment Galois Group for $x^5-1$
Better yet; if $\rho^3(\zeta)=\zeta^4$ then $$\rho^3(\zeta^2)=(\rho^3(\zeta))^2=(\zeta^4)^2=\zeta^8=\zeta^3.$$ So it seems that $\omega=\rho^3$.
18h
comment Frobenius on projective variety is not an isomorphism?
The fourth statement tells you that $\phi$ is the identity precisely on the $\Bbb{F}_q$-valued points of $V$. This suggests it isn't the identity on all points of $V$. What is your definition of $\Bbb{P}^n$?
2d
comment Residue of $\frac{1}{(1-z)^3}$ at $z=1$
The function $h(z)=(1-z)^3$ has a zero of order $3$ at $z=1$.
2d
comment A question of cosets
Hint: It is also true if $G$ is not assumed to be finite.
2d
comment A question of cosets
What are your thoughts on the question?
2d
revised for what integers $x$ do there exist $x$ consecutives integers, the sum of whose squares is prime?
Corrected mistake, elaborated on solution.
2d
revised for what integers $x$ do there exist $x$ consecutives integers, the sum of whose squares is prime?
Corrected mistake, elaborated on solution.
2d
comment for what integers $x$ do there exist $x$ consecutives integers, the sum of whose squares is prime?
Thanks, I just noticed, but my battery died. I'll be making some revisions.
2d
comment for what integers $x$ do there exist $x$ consecutives integers, the sum of whose squares is prime?
Is this a question? If so, I don't understand what you're asking.
2d
revised for what integers $x$ do there exist $x$ consecutives integers, the sum of whose squares is prime?
deleted 1 character in body
2d
answered for what integers $x$ do there exist $x$ consecutives integers, the sum of whose squares is prime?
2d
comment Matrix multiplication question (diagonal matrices)
For your first question; no. Consider the matrices $$A=\binom{1\ 0}{0\ 1}\qquad\text{ and }\qquad B=\binom{0\ 1}{0\ 0}.$$ For your second question; not that I know of.
2d
comment If A denotes the union of these cosets formed by the elements of a subgroup of the quotient group H, show that A is a subgroup of G.
The elements of $G/N$ are cosets of $N$ in $G$. Because $H$ is a subgroup of $G$, its elements are also cosets of $N$ in $G$, but not necessarily all cosets of $N$ in $G$. So the approach you suggest is not right.
2d
comment Matrix multiplication question (diagonal matrices)
They are matrices; do not trust your feeling.
2d
answered Matrix multiplication question (diagonal matrices)
2d
comment Cylic group of order 2
Take your two favourite groups $A$ and $B$ of order two. There are two group homomorphisms from $A$ to $B$. One is the zero map, the other is an isomorphism.
2d
answered What is the index of $\mathrm{diag} G$ in $G \times G$ if $G$ is a finite group?
Apr
21
comment An easy proof that $\mathrm{SL}(n,F)$ is irreducible in the Zariski topology
If your field isn't algebraically closed, then you should be careful about what you mean by $\mathcal{I}(\mathcal{V}(\det-1))$. What are your definitions of $\mathcal{V}(I)$ and $\mathcal{I}(V)$ for ideals $I$ and algebraic sets $V$?
Apr
21
comment An easy proof that $\mathrm{SL}(n,F)$ is irreducible in the Zariski topology
In a unique factorization domain, a principal ideal generated by an irreducible element is prime. The ideal $\mathcal{I}(\mathcal{V}(\det-1))$ is the radical of the ideal $(\det-1)$, which is $(\det-1)$ itself whenever $(\det-1)$ is prime.
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