I wanted to post this question because I know a lot of the posters here are professors themselves. So I'm applying to math phd programs and I've been asking profs to write me rec's.
My question is why professors insist that I waive my right to see the recommendations. I asked them if they...
i'm working through the following text and I think I found an error please let me know if I'm totally wrong.
Janusz, Gerald J. Algebraic Number Fields
and I'm starting with the 3rd exercise on page 3. It is as following:
let R be an integral domain and p a prime ideal of R. Show there...
I've been trying to prove something that seems obvious but have had no success thus far:
say G is a finite group and H and K are proper subgroups, if K contains a conjugate of H, then it isn't possible to have G=HK.
Proof anybody? I'm happy if one can prove the special case below:
It's...
A general question.
A unit element is one that has it's multiplicative inverse in the ring.
An element p is prime if whenever p=ab then either a or b is a unit element.
Can a prime be a unit element?
The answer is, i think, no but thus far I've been unable to find a contradiction.
it is a theorem that for dimensions three or higher euclidean space cannot be turned into a field, or if we want to be pedantic: for n >/= 3 there is no field isomorphic to R^n.
I saw a proof of the fact in a complex analysis class sometime ago so I don't remember it but it uses (very)...
i was going to state the false claim: integral domains of finite characteristic are finite.
An indeterminate, ok.
I presume F_p is the field of 0,1,...,p-1 where addition is modp and similarly for multiplication. If you could elaborate as to 1. what the algebraic closure of F_p is, 2. how it...
take the finite ring J_17 (addition mod 17 and multiplication mod 17). Consider the set of polynomials in one variable X (which, say, runs through the real line) with coefficients from J_17. This set of polynomials is a ring: all the ring axioms can be verified using the fact that J_17 is a ring...
So I'm looking for an example of an infinite integral domain with finite characterestic. That is a infinite integral domain such that there is a prime p such that p copies of any element added together is the additive identity.
I'm just looking for a simple counterexample. I'm working...
Ok, so there is this strange phenomenon that I have experienced several times before. I want to know if anyone else here has had this problem or if they have any idea what it might be. AS A RESPONSE TO THE ABOVE DISCLAIMER: I will not consider any response as a diagnosis but as of now the...
Consider a sequence of sets, A_n. If an element x in not in the union of this collection of sets then it is not inside ANY set in this sequence of sets. (*)That means it is in the compliment of every set contained in the sequence of sets ie the intersection(*). We have shown the LHS is contained...
really? lol, i thought i was simplifying things. I AM thinking of linear independence of columns/rows, but I can't count all combinations of linearly independent columns/rows in a straightforward fashion.
This is the last problem on herstein's 2.3 problem set.
So we want to count how many 2x2 matrices with entries being integers mod p have nonzero determinant mod p. p is prime.
for p=3 there are 48 such matrices. I've broken the general case into three possibilities: matrices with no...