Recent content by calvino

Thank you. I don't know why I tend to forget my basics. Perhaps that is my tragic flaw. Nothing seems to be retained anymore. I should rethink my studying strategies. Thanks again. EDIT: and sometimes I get flustered by thinking a question is too complex, that I do not know where to start...

Homework Statement This question is from my text. a)show that the splitting field of (x^4)-5 over Q is Q(5^(1/4), i). b)show that [Q(5^(1/4), i): Q = 8]. c)what is the order of the galois group of (x^4)-5 over Q? The Attempt at a Solution I haven't yet thought about b) and c). For...

that's right. it has order 2. the actual question talked of the cube root of 3, and not the sqrt. I mistakingly thought It would be similar if I used the latter. So by the same method I can show that the cuberoot of 3 must be sent to the cuberoot of 3. Thank you. I will try it out now.

How does one show that the order of Gal(Q(SQRT3)/Q) is 1. I mean, I understand that all the elements of Q (irrationals) will stay fixed, and that really only leaves one mapping of SQRT3 to itself as well, but I don't know how one would construct a proof. any help would be great.

Like in the title, I'm trying to prove that if a^2 is algebraic over F, then a is algebraic over F. my idea- by assumption, a^2 is a solution to the polynomial equation b_n x^n + b_(n-1) x^(n-1) + ... + b_0 = 0 , b_n's are in F if a^2 is in F, then we simply write a^2=a *a, and...

can we use the fundamental theorm of homomorphisms? i didn't. i simple constructed a diagram of the homomorphisms involved and showed that since psi.j is in a sense doing the same things as phi is, then they method is unique.

i understand how to define the function (i think). Am i suppose to see it's uniqueness, naturally?

I've already completed 1), but it's necessary for one to know it for question 2). I'm pretty sure that I've found my homomorphism in 2, but I don't know whether or not is unique. How do I show a homomorphism is unique in this case? Problem 1: Let R be a commutative unital ring, and let S be a...

weird...im pretty sure i responded to this thread twice earlier. ircdan..thanks for your input no 1). i did learn something from it, and I decided to apply it to 2). I guess I shouldn't have tried to make the sequence first. for 2), i got a generating funtion (in a sense), but it is...

I'm unsure about the following questions. Theyre from my introductory combinatorics class. 1) Let a_n denote the number of ways to distribute n objects to three people: A, B, C. A must have at least 2 of the objects, and B must have an amount divisible by 5. Find the generating function of...

yes, i figured out that the symmetry of the square did work. however, for the first part, i messed up and somehow assumed ba=ab. the way i attempted to prove it was by claiming certain elements were the generators of the set, and by trying to show just that. obviously getting ab=ba (somehow!)...

ok so i showed that the function given in the hint was a homomorphism (straight from definition), and now I'm just going to show that it is 1-1, by proving something about the kernel. thanks for the help again. now, as for 1)...im unsure of how or which group has EXACTLY 8 elements. like i...

just to show my progress in 2).. what i did was show that the commutator was an element in K, and that it is in H, using the definition of Normal in G. this made it e. thanks for the hints, though I am sure you might think you've overhinted. i appreciate it though. ill keep you all updated...

thanks..i think i have it. looking over 1 though, today, I'm confused with the "at most" elements, and finding the group with exactly 8 elements. firstly, i thought that I would be able to find all 8 elements needed for part a, and that there would be 8. second of all, does part b mean that...

oh sorry...i never used a theorem involving commutator. looked it up now. i'll work on it and reply in a few hours...thanks for your help. edit: i don't think we can use theorems nor definitions that haven't been taught in class. is there another way to prove the commumativity?