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Dec
8
comment Solvability of Artin-Schreier Polynomial
Being solvable by radicals doesn't require the splitting field itself to be a radical extension, but only to lie in a radical extension.
Dec
2
comment Assume we have $\mathbb{Z}_{p}[x]$ with $p$ being a prime. Prove that $x^{p-1}-1=(x-1)(x-2)…(x-(p-1))$
@AndréNicolas: in ${\mathbf Z}_3[x]$, $x^2$ and $2x^2-1$ each have degree $2$ and their difference $x^2-1$ has 2 distinct roots but is not the zero polynomial (Pedro made a comment while I was about to write the same thing, so I give an example instead.)
Nov
28
comment How do I go with proving that the coefficient of each terms of $\prod^{k=n}_{1}{1-x^k}$ is either 1,-1 or 0?
This is a famous result called the pentagonal number theorem. Googling that term will show you a formula for the coefficients that are $1$ and $-1$, which will provide a pattern for them.
Nov
28
comment Primes of the form $p=a^2-2b^2$.
You need Alvaro's original condition $p \equiv 1 \bmod 8$, not just $p \equiv 1 \bmod 4$, to handle the case $q = 2$.
Nov
28
comment Polynomials over $\mathbb{F}_2$ without multiplicity 1 factors
Since $k(x) = k(1/x)$ but $k[x] \not= k[1/x]$, you can't really speak about "the" ring of integers in a function field; such a ring always depends on a choice of places to be integral away from (i.e., it's a ring of $S$-integers for some $S$). The Mason--Stothers theorem generalizes to arbitrary function fields, with additional terms involving the genus. See Chapter 7 of Rosen's "Number Theory in Function Fields."
Nov
26
comment Show that $x\otimes x+2\otimes2$ is not an elementary tensor in $I\otimes_{A}I$
This has been asked before: math.stackexchange.com/questions/823642/…
Nov
26
comment Galois group of a polynomial and subfields
Find an example or show there are no examples. Use Galois theory to think about properties of such an example as in (b) in terms of group theory.
Nov
26
comment Proving uniqueness of $e$
This argument assumes that the definition of $f(a)$ makes sense, i.e., that $\lim_{h \rightarrow 0} (a^h - 1)/h$ exists in the first place.
Nov
26
revised Polynomials over $\mathbb{F}_2$ without multiplicity 1 factors
edited body
Nov
25
answered Polynomials over $\mathbb{F}_2$ without multiplicity 1 factors
Nov
25
comment If the commutator of a finite group has order $2$, then the order of the group is divisible by $8$
See Qiaochu Yuan's answer (currently it is number 6) at mathoverflow.net/questions/23478/….
Nov
25
comment Quotient field of gaussian Integers
Yes. And the term is equivalence classes, not equivalent classes.
Nov
25
revised Measure Theory Problems
added 1 character in body; edited title
Nov
25
comment Quotient field of gaussian Integers
Your definition of the quotient field as pairs $[a,b]$ subject to a certain equivalence relation has nothing to do with $a$ and $b$ being integers. It works the same if they are Gaussian integers, or elements of any integral domain at all.
Nov
20
comment Undergraduate Research Ideas?
Oh, transform theory, not transformation theory.
Nov
20
revised What is the meaning of “Hermitian”?
added 7 characters in body
Nov
20
comment Undergraduate Research Ideas?
While the previous comment is on the mark, I am curious: what exactly is "Transformation Theory"? Every other course title looks familiar, but not that one.
Nov
20
comment A question in Abstract Algebra about cosets
The left or right cosets of a subgroup are not themselves always groups, so I changed your post to speak of a set of cosets, not a group of cosets. Also, learn how to spell the word coset.
Nov
20
revised A question in Abstract Algebra about cosets
deleted 5 characters in body; edited title
Nov
20
comment Evaluate $\int_0^1 \frac{x^k-1}{\ln x}dx $ using high school techniques
IdrisAddou, asking for solutions that include justification of analytic manipulations like swapping the order of summation or integration is going beyond the pre-university level. The posted solution using differentiation under the integral sign includes no justification for why that method fits this application, and to do so would go beyond the level of high school. To some extent a certain amount of "handwaving" in the derivations should be allowable at the level at which you are asking the question.