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Feb
5
comment Is $\mathbb{Z}[x]/(x^2 + x + 1, 9)$ isomorphic to $\mathbb{F}_{81}$?
Your reaction that $\mathbb Z/9$ is not a field is good... But, there might be a trick, that "3" got killed off (somehow, implicitly, if someone was trying to prank you, etc. ... or if Nature had turned against you... :) ... but that is not decisive. :)
Feb
4
awarded  Populist
Feb
2
answered How do I solve the following equation: $z^4+z^3+z+1=0$
Feb
1
comment Notation: $\mathbb{Z}[\sqrt{-5}]$
I guess you and I are in different worlds of mathematical usage. I agree that square roots of negative numbers oughtn't be introduced to early... but in introductory abstract algebra or introductory algebraic number theory, writing $\sqrt{-5}$ or $\sqrt{-1}$ is certainly conventional usage. Not for grade-schoolers, no. Also, $\log(-1)$ is $\pi i$ ambiguous by multiples of $2\pi i$. Care is required, but it has sense. I think at the level of the question, $\mathbb Z[\sqrt{-5}]$ is apt, and is at least completely standard.
Feb
1
comment Notation: $\mathbb{Z}[\sqrt{-5}]$
No, it is certainly not obsolete at all. (The possibility of mis-using products of square roots is irrelevant, and bringing $\sqrt{-1}$ into the picture doesn't help anything.)
Feb
1
comment Notation: $\mathbb{Z}[\sqrt{-5}]$
There's no reason to write $\sqrt{-5}$ as $i\sqrt{5}$...
Feb
1
revised Legendre symbol, what is it?
edited title
Jan
30
comment Formula for this pattern?
Certainly IQ-test questions in this vein do not reliably have genuine content, if a sequence arises in the course of doing something else (one could tell what that was), there is a much reduced ambiguity if one asks for sequences whose description has the lowest possible (Kolmogorov-etal) complexity. E.g., taking consecutive differences, and differences of differences, etc., until all the differences are 0 (whether or not this occurs earlier than expected/hoped) produces the lowest-degree polynomial interpolation. @BrianM.Scott's observation suggests that a polynomial interpolation is not apt.
Jan
29
answered What is the minimal correction to the harmonic series such that it converges?
Jan
26
awarded  Necromancer
Jan
24
answered Non-associative commutative binary operation
Jan
24
comment Non-associative commutative binary operation
This is an important example, but the genuine problem here is that convolution of distributions is not really definable in general... Convolution of compactly-supported distributions does work alright, because compactly-supported distributions are provably derivatives of continuous functions, etc.
Jan
22
answered (Distributional) Fourier transform
Jan
19
comment Why doesn't Fermat's Last Theorem for polynomials entail that for integers?
Apart from confusion over quantifiers and such, it is still a very interesting question why ... somehow... the one instance (perhaps seemingly more sophisticated/complicated) of "Fermat's Last Theorem" doesn't imply Wiles' Theorem... somehow.
Jan
19
comment Why the terminology “global fields” and “local fields”
@peterag, I don't think Hensel in 1896 operated in the sort of abstraction that would have led him to talk that way, at all, although I may be wrong. (I don't think he used the specific word "local" or "lokalsche" or anything.) Also, Frechet's work seems not to have had much impact for a while after... I'd wager that the terminology is post-EmmyNoether, for example...
Jan
19
comment Why the terminology “global fields” and “local fields”
@peterag, it is certainly true that "local fields" in the number-theoretic sense are locally compact, I don't think that is the origin of the modifier "local", but as QiaochuYuan notes, it is from physical local-ness. As in "local ring", which no longer entails local compactness.
Jan
18
comment What are the primes in quadratic integer ring $\mathbb{Z}[D]$
Also, quadratic reciprocity tells which primes will split.
Jan
16
answered Prove that if an integer $z$ is not divisible by $p$, then it is invertible in the $p$-adic integer ring $\mathbb{Z}_p$.
Jan
14
answered Importance of the compactness of idele group
Jan
12
awarded  Revival