
Please post any and all homework or other textbookstyle problems in one of the Homework & Coursework Questions...

Feb2313 09:24 AM
micromass

1 
36,194 
I am trying to figure out if the polynomial is reducible over Z5 and also over Z.
For Z5, i tried:
f(0) = 1 ...

Dec1108 12:38 PM
billybob12345

3 
5,013 
Describe the field F=\frac{\mathbb{F}_3}{(p(x))} p(x) is an irreducible polynomial in \mathbb{F}_3]. Find an element...

Dec908 11:46 PM
adriank

2 
1,272 
im teeching algebra and had to prove that X^5  8 was irreducible over the rationals. so i did it using eisenstein.
...

Apr2006 06:50 PM
mathwonk

4 
4,077 
I've been trying to work out a bunch of problems that have to do with finding irreducible polynomials, and this one...

Jul2509 09:25 AM
g_edgar

1 
2,047 
Basically, i am doing some cryptography, i need to show that a polynomial i have, which is not irreducibale, implies...

Jun2210 07:49 AM
ohubrismine

3 
1,854 
Can someone explain to me why the following is true (ie, show me the proof, or at least give me a link to one):
...

Aug2208 05:01 AM
sd522527

15 
10,891 
Hi, yet another question regarding polynomials :). Just curious about this.
Let f(x), g(x) be irreducible...

Jun1511 08:21 PM
burritoloco

5 
1,419 
Is it true that polynomials of the form :
f_n= x^n+x^{n1}+\cdots+x^{k+1}+ax^k+ax^{k1}+\cdots+a
where...

Nov2611 08:32 AM
COURAGE_WOLF

5 
2,000 
I am attempting to construct a field containing 625 elements and should be in the form Zn mod f(x).
Factoring 625...

Nov907 03:09 AM
matt grime

1 
4,786 
okay so i was reading a book on representations and found this discussion and was confused:...

Jan2210 08:29 AM
wofsy

3 
4,946 
Hi guys, I have a question which is very fundamental to representation theory.
What I am wondering is that whether a...

Jul2410 06:35 PM
nematic

0 
1,665 
All commutative groups have one dimensional representation
##D(g_i)=1, \forall i##
I understand what is...

Jan1014 08:40 AM
Office_Shredder

14 
1,119 
So I'm studying molecules and symmetry and I was wondering if there was a intuitive way of understanding why there are...

Oct1610 10:34 AM
sineontheline

1 
1,063 
Does anyone know how to classify the finitedimensional irreducible representations of so(4,C)? Can they all be built...

Aug609 05:08 PM
aziz113

2 
2,891 
Hi all,
The representations S^1 = \mathbb{R}/\mathbb{Z} \to U(1) are of the form \rho_n : \mapsto e^{2\pi i n x}...

Feb208 11:08 PM
jdstokes

1 
1,644 
Proposition. A polynomial of degree 2 or 3 over a field F is reducible iff it has a root in F.
Tell me if I'm on...

Nov1809 05:51 AM
HallsofIvy

1 
767 
If you were to tell me that "range" and "span" meant the same thing I would understand why, in english their meaning's...

May2212 07:58 PM
alexfloo

29 
3,054 
I'm really confused... we refer to the "size" of a group as the "order"... But are they really equivalent? Can we...

Oct3112 06:39 PM
micromass

2 
898 
In set theory, we may define a function A > B to be a relation on AxB that is "single valued": to each a in A there...

Sep2209 08:21 AM
Hurkyl

0 
739 
We all know the definition of prime numbers and the first prime number is always 2.
Why is 1 not listed as a prime...

Jul2305 01:53 PM
Hurkyl

25 
5,778 
Hi, not sure if this is the right forum.. pls move if not.
Almost 30 years ago, I was studying engineering and my...

Nov1811 05:54 PM
narrator

6 
2,627 
Am I missing something or is 0 a prime element in an integral domain?
In the definition of prime element p of an...

Feb2808 10:17 PM
mathwonk

8 
1,561 
Hi there, this is my first post here so I'm sorry if this is in the wrong place, asked before, standard newbie...

Oct2011 06:12 PM
D H

34 
6,004 
At first, when I saw this, I was deeply shocked and lost the believe that math is absolute. Like the thinking that if...

Jan1609 04:59 PM
HallsofIvy

4 
3,224 
I've heard ppl say it is and it isn't, so is it a prime number? :P

Feb204 06:52 PM
mathman

3 
2,648 
Can some one tell me how to figure out if this is solvable or not?
For the Prime number p=68659,
19=x^2 mod p.
...

Dec1107 02:11 PM
robert Ihnot

12 
2,435 
scratch that.
is 5606701775893 a prime number?

Jun111 09:10 PM
ramsey2879

19 
5,731 
Is any given finite semigroup isomorphic to some finite semigroup S that consists of some subsets of some finite group...

Jul2413 07:13 PM
micromass

4 
602 
Hi,
I'm not sure if this is the right section, but I'm talking about numbers :).
The questions is as written in...

Oct2511 02:48 PM
lavinia

26 
3,413 
I was reading Lie Algebras in Physics by Georgi.......................second edition...
Theorem 1.2: He proves that...

Dec2409 03:15 AM
krishna mohan

3 
5,419 
I don't know how to write out matrices nicely on this forum,
but suppose you have some matrices:
This...

Nov512 01:54 PM
micromass

1 
708 
I've been working on this Linear Algebra problem for a while: Let F be a field, V a vector space over F with basis...

May2612 11:23 AM
imurme8

2 
1,088 
Can someone confirm this? If so, are there any respected websites on the net that can confirm this theorem?

Aug509 09:06 PM
D H

1 
767 
If V is a vectorspace and v is a vector in V. will the projection of v onto V be v?

May712 03:34 PM
tinytim

1 
883 
A vector space is a collection of vectors. So can we say that it is a set (although with special properties) ? Just...

Jan2211 12:37 PM
sponsoredwalk

20 
5,618 
According to wikipedia, absorption is an axiom for a boolean algebra. This seems incorrect to me, since I believe...

Oct913 02:48 PM
mfb

3 
856 
Is an infinite series of random numbers possible?
That is, can the term "random" apply to a infinite series?
...

May212 04:42 AM
micromass

89 
13,593 
Hello,
If f is a morphism between two vector spaces, we say it is linear if we have:
1) f(x+y) = f(x) + f(y)
2)...

Dec809 06:20 PM
DrGreg

7 
8,361 
Hi..
In the second paragraph of the following paper, there is a statement: "Because the direct product of subgroups...

Jun2410 01:06 PM
Landau

1 
1,742 
hi there. I have an equation i derived from a "belt problem" (i actually dont know if it's correctly derived yet)....

Apr810 09:26 PM
Live2Learn

5 
1,429 