afedder

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	252 reputation	bio	website		visits	member for	1 year, 1 month
17 badges		location			seen	Jan 9 at 21:55

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Apr 21	awarded	Yearling
Dec 14	accepted	Rank of Linear Operators Applied to Polynomial
Dec 13	comment	Rank of Linear Operators Applied to Polynomial @MattN. when I say conjugate, I mean there exists an invertible linear map $R$ such that $T=RSR^{-1}$
Dec 13	comment	Rank of Linear Operators Applied to Polynomial @froggie $f(T)$ and $f(S)$ would be conjugate as well...but how would this help with rank?
Dec 13	comment	Rank of Linear Operators Applied to Polynomial @MattN. what the heck is $A$?
Dec 13	asked	Rank of Linear Operators Applied to Polynomial
Dec 12	asked	Notation Two Headed Arrow
Dec 7	accepted	How does one prove that a polynomial has no rational roots in general?
Dec 7	comment	How does one prove that a polynomial has no rational roots in general? The reason to use more advanced stuff is because that is the course I am in, modern algebra. The point is that I already understand this theorem under the typical "high school" guise. However, it another context, it can be harder to grasp.
Dec 7	comment	How does one prove that a polynomial has no rational roots in general? Is there a way to get the results of this theorem in order to use it without actually proving it in detail from the link? In other words, can you derive these results about possible rational roots by just considering $\mathbb{Z}[x]$ as a UFD?
Dec 7	comment	How does one prove that a polynomial has no rational roots in general? Got it, thanks!
Dec 7	comment	How does one prove that a polynomial has no rational roots in general? What I meant is, first and foremost, the only factors that a rational root depends on is those of $a_0$ and $a_n$? In other words, there is no rational roots that might "slip through the cracks" of this possible list? More generally, would there be any exceptions to the application of this theorem?
Dec 7	accepted	Can the Euclidean algorithm prove Euclid's Lemma in a UFD?
Dec 7	comment	How does one prove that a polynomial has no rational roots in general? So each rational root ONLY depends on $a_0$ and $a_n$?
Dec 7	comment	How does one prove that a polynomial has no rational roots in general? First of all, I don't know what the rational roots theorem is. Second of all, how would you prove this generally? I have a few more examples that I need to prove and I don't know how to begin.
Dec 7	comment	Can the Euclidean algorithm prove Euclid's Lemma in a UFD? So you don't need a prime factorization argument?
Dec 7	comment	Can the Euclidean algorithm prove Euclid's Lemma in a UFD? Since $A$ is a UFD, we can let $a=p_1p_2...p_n$ for some primes $p_1,p_2,...,p_n \in A$. Then, for all $i$, $p_i$ does not divide b. But I don't know how to proceed.
Dec 7	comment	Can the Euclidean algorithm prove Euclid's Lemma in a UFD? so how would you go about proving it then?
Dec 7	asked	How does one prove that a polynomial has no rational roots in general?
Dec 7	asked	Can the Euclidean algorithm prove Euclid's Lemma in a UFD?