61,730 reputation
453129
bio website
location
age
visits member for 3 years, 5 months
seen 9 mins ago

3h
comment If a polynomial $g$ divides $f$ and $f'$, then $g^2$ divides $f$?
Dear @Jim: I certainly agree that there is no room on this site for rude personal remarks (quite independently of the thread here, about which I'd prefer not to contribute any more).
3h
answered If a polynomial $g$ divides $f$ and $f'$, then $g^2$ divides $f$?
4h
comment If a polynomial $g$ divides $f$ and $f'$, then $g^2$ divides $f$?
Dear @Jim, Zarrax has written an excellent and complete answer to Artin's exercise. It will be useful to the OP and other users. Your answer is quite interesting too and has rightfully been strongly upvoted . There is however no need to be unduly critical, and there is ample place for both answers on this site.
4h
comment If a polynomial $g$ divides $f$ and $f'$, then $g^2$ divides $f$?
"...since $g$ is irreducible" and $char.F=0$
1d
answered Let $F$ be a field of characteristic $p$ and let $f(x)=x^p-a\in F[x].$ Show that $f(x)$ is irreducible over $F$ or $f(x)$ splits in $F.$
1d
comment Let $F$ be a field of characteristic $p$ and let $f(x)=x^p-a\in F[x].$ Show that $f(x)$ is irreducible over $F$ or $f(x)$ splits in $F.$
Dear Amr: it's a special case , but it is definitely not trivial nor just a comment. Especially if you have never heard of the Frobenius map, which you then have rediscovered :-) Anyway, +1
1d
comment Let $F$ be a field of characteristic $p$ and let $f(x)=x^p-a\in F[x].$ Show that $f(x)$ is irreducible over $F$ or $f(x)$ splits in $F.$
@Amr: thanks for answering. I asked because you are so enthusiastic about the question: which is all to your credit!
1d
comment Notation question A $\subset \subset B$
Dear @B11b: I'm sorry to say that I don't think I'll address it.
1d
comment Let $F$ be a field of characteristic $p$ and let $f(x)=x^p-a\in F[x].$ Show that $f(x)$ is irreducible over $F$ or $f(x)$ splits in $F.$
Dear @Amr: are you user144258?
1d
comment Let $F$ be a field of characteristic $p$ and let $f(x)=x^p-a\in F[x].$ Show that $f(x)$ is irreducible over $F$ or $f(x)$ splits in $F.$
Being clueless is normal: this is a difficult result.
1d
comment Let $F$ be a field of characteristic $p$ and let $f(x)=x^p-a\in F[x].$ Show that $f(x)$ is irreducible over $F$ or $f(x)$ splits in $F.$
By the way, if $p$ is a prime number and $F$ is a field of arbitrary characteristic (for example characteristic zero) the polynomial $x^p-a\in F[x]$ is irreducible as soon as it has no root in $F$.
1d
comment Notation question A $\subset \subset B$
@Daniel: oops, you are right: I misstated what I meant. Now corrected. Also, I assume that the ambient space $X$ is indeed Hausdorff. As an algebraic geometer I work with non Hausdorff spaces all the time, but then I call quasi-compact a space having finite subcoverings for open coverings. A compact space is then a Hausdorff quasi-compact space. But since in real or complex finite-dimensional analysis (in particular in Hörmander's book) spaces are Hausdorff, I didn't want to go into this distinction between compact and quasi-compact. Anyway, thanks for your comment.
1d
revised Notation question A $\subset \subset B$
deleted 15 characters in body
1d
answered Notation question A $\subset \subset B$
2d
answered Show that there is only one conic passing through the five points $[0:0:1], [0:1:0],[1:0:0],[1:1:1]$ and $[1:2:3]$. Show that it is nonsingular
2d
comment The form of subrings of $k[[t]]$
Dear Magdirag: I agree. The exercise is poorly formulated, to say the least: we shouldn't be left trying to guess what the author means.
2d
comment The form of subrings of $k[[t]]$
Dear B11b, unfortunately I can't explain anything because I don't even understand the statement! By the way from what book is this extracted?
2d
comment The form of subrings of $k[[t]]$
Dear Magdiragdag, $H = {\mathbb Z}[[t]]$ is not closed under "formal sums": what is the "formal sum" of $1,1+t, 1+t+t^2,\cdots$ ?
2d
comment The form of subrings of $k[[t]]$
I don't understand what the exercise means: no subring of $k[[t]]$ contains the formal sums of its elements, and neither does $k[[t]]$. What is the formal sum of $1,1+S_1,1+S_2,\cdots$ ?
2d
comment Need an explanation for homomorphism in commutative algebra
1) You should name the authors of your book 2) What you highlight is your condensation of the problem. The authors split their exercise in five parts and what you quote is only the fourth. If you want users to help you, don't make it more difficult for them than it already is.