16,850 reputation
12045
bio website math.brown.edu/~lubinj
location Minnesota
age 78
visits member for 3 years, 5 months
seen 3 hours ago

Aged mathematician


19h
comment Why are separable and normal field extensions so called?
It would be delightful if every property had a name that was reasonably descriptive. In the case of “normal”, this is unfortunately not the case.
19h
comment If K is a perfect field, is any extension of K also a Galois Extension?
It’s certainly true that any algebraic extension of a perfect field is perfect.
1d
answered Additive inverse of elements in the p-adic numbers $\mathbb Q_p$
1d
comment Additive inverse of elements in the p-adic numbers $\mathbb Q_p$
Are you doubting that $\Bbb Q_p$ is a field?
1d
answered Ring homomorphism takes discriminant to discriminant
1d
comment Ring homomorphism takes discriminant to discriminant
I think that the discriminant of $X^2+1$ is $-4$.
2d
comment Find finite field GF(31)
In total agreement with @MJD, I would say that there is no polynomial that you should be considering. GF(31) is precisely $\Bbb Z_{31}$, end of story.
Mar
24
answered Algorithm to determine if a given polynomial over $\mathbb{Q}$ is irreducible over the $p$-adic number field
Mar
23
comment Algorithm to determine if a given polynomial over $\mathbb{Q}$ is irreducible over the $p$-adic number field
I like this question, because I ought to know the answer, and don’t.
Mar
22
comment Exponentiation in Modular Arithmetic
Please note that if you're asked to solve the congruence, you should be finding all $a$’s that make the congruence true, not just the obvious one. And you do understand, don't you, that the $a$ in question is an ordinary integer, not something to be read modulo 17?
Mar
22
comment cardinality of polynomial
There are a few theorems you should be aware of. For instance, that if $A$ and $B$ are countable, then so is $A\times B$.
Mar
22
comment cardinality of polynomial
You should tell us what you know and what you've tried so far.
Mar
22
comment How to compute the fixed field of an automorphism?
In that case, let me give you a general strategy: when you have a subgroup, you should always try the trace and the norm of your generating element. Norm is no good here, but you'll see that $\omega+\omega^{-1}$ does the trick for you.
Mar
22
comment How to compute the fixed field of an automorphism?
I don't think that $\sigma$ is of order two.
Mar
21
comment Suppose $1 = ar + bs$, show $bs = 1 \mod r $ and $bs = 0 \mod s$
You need to know what $A\equiv B\pmod m$ means. Once you do, you’ll see why your question is easily answered. So my recommendation to you is to review precisely what congruence means. Indeed, the fact that you used an equals sign rather than a congruence sign tells me you need to go back.
Mar
21
answered Number of finite extensions of $p$-adic number field of given degree $n$
Mar
19
answered Show that the splitting fields of $x^3 - 2$ and $x^3 - 3$ are not equal
Mar
18
answered Confusion with Lang's proof of Sylow Theorem
Mar
17
answered Matrices and Galois groups
Mar
17
comment Matrices and Galois groups
Let me try to put it into an answer.