Recent content by mathjam0990

Question This is what I have done so far. I was wondering if anyone could verify that I found the correct minimum polynomial and roots? If I am incorrect, could someone please help me by explaining how I would find the min polynomial and roots? Thank you.

Very helpful information, thank you!...if I could ask one more question, say we have the polynomial x4+x3+x2+x+1 and we wanted to find a splitting field over ℚ. Could we approach this by recognizing that this is the minimum polynomial of Φ5(x) thus root ϑ = e2πi/5. So the minimum polynomial is...

Let f(x)=x4-2x2+9 Find the splitting field and Galois group for f(x) over ℚ Here is what I have written out so far. If I have found the splitting field E correctly, have I proceeded with the Gal(E/F) group correctly? Also, how would I go about finding the roots of this equation by hand...

Thank you very much. This was helpful!

Thank you for your response. I apologize, I should have mentioned that I knew the proof would be to show each is contained in the other. But I have no clue how to show $\zeta_p \in \mathbb{Q}(\zeta_p^i)$. Could you please explain how I would do that and I can respond via "reply with quote" if I...

Let ζ5 be e2πi/5. Find a monic polynomial of degree two in K(ζ + ζ−1) So, if E/F is a field extension, with α∈E then K(α) = {f(x)∈F[x] | f(α)=0} and m(x) is the minimal polynomial of α over F such that K(α) = [m(x)] where [m(x)] is the ideal generated by m(x). I was thinking maybe (x- ζ -...

Let ζp be e2πi/p. For an integer i, such that p does not divide i, prove Q(ζp) = Q(ζip ). I think this has something to do with both exponents of ζp (1 and i) being coprime to p, but I am not sure at all how to show the equality. If anyone could please help with an explanation, that would be...

What I have done so far... Is this correct so far? If not, would someone be able to provide an explanation as to how to solve this? I am not sure if I am going in the right direction. Thank you

Firstly, I cannot thank you enough for taking the time to write out this detailed explanation. We covered majority of what you said in my lecture, but you provided some essential key points that were not mentioned by my professor which kind of helped to tie this altogether much better. I...

Thank you for relocating my thread to the correct location. I do love this forum and it's very helpful to me and my studies! However, for my level, I believe that one-on-one interaction (live help in real time) would be best for me. It would be easier to hear someone's voice and watch them break...

Let, E={a+bw : a,b in ℚ) ⊆ ℂ w = -1/2 + [√(3)/2]*i ∈ C Prove: E is closed under addition, subtraction, multiplication and division (by non zero elements) Prove: E ≅ Q[x]/(x2+x+1) Is the goal to show that for any two elements in E, all 4 operations can be performed...

Describe the multiplication in the ring Q[x]/(x2+x+1). Is this a field? What is the multiplicative inverse of [x]? In describing the multiplication, would I just be describing something in regards to the multiplicative properties of a ring? i.e: a(bc)=(ab)c a(b+c)=ab+ac a*1=1*a=a ab=ba Is it...

Hello, I was wondering if anyone knows of any legitimate websites (companies) that offer tutoring in college level abstract algebra and real analysis? If anyone knows any information or resources I should consider that would be great! Thanks in advance

Express r12+r22+...+rn2 as a polynomial in the elementary symmetric polynomials s1, s2, . . . ,sn. I'm sure the equation we are dealing with is (r1+r2+...+rn)2 which is very large to factor out but should yield r12+r22+...+rn2+(other terms) I believe s1=r1+r2+...+rn s2=Σri1ri2 for...

This is the part I wasn't seeing! Thanks a lot for breaking that down!