Question

Let E be an extension of F, and let S be a subset of E.IfF(S) is...

Let E be an extension of F, and let S be a subset of E.IfF(S) is the subfield of E
generated by S over F, in other words, the smallest subfield of E containing F and S,
describe F(S) explicitly, and justify your characterization.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let F⊆K⊆E be extension fields. If K is an algebraic extension of F and let α∈E...
Let F⊆K⊆E be extension fields. If K is an algebraic extension of F and let α∈E be algebraic over K. Show that α is also algebraic over F.
Let E/F be a field extension, and let α be an element of E that is...
Let E/F be a field extension, and let α be an element of E that is algebraic over F. Let p(x) = irr(α, F) and n = deg p(x). (a) For f(x) ∈ F[x], let r(x) (∈ F[x]) be the remainder of f(x) when divided by p(x). Prove that f(x) +p(x)= r(x)+p(x)in F[x]/p(x). (b) Prove that if |F| < ∞, then | F[x]/p(x)| = |F|n. (For a set A, we denote by |A| the number of elements in A.)
Let E/F be an algebraic extension. Let K and L be intermediate fields (i.e. F ⊆...
Let E/F be an algebraic extension. Let K and L be intermediate fields (i.e. F ⊆ K ⊆ E and F ⊆ L ⊆ E). (i) Prove that if the extension K/F is separable then the extension KL/L is separable. (ii) Prove that if the extension K/F is normal then the extension KL/L is normal. Note: To make things easier for you, you can assume that E/F is finite (hence all extensions are finite),
Let E/F be a finite Galois extension such that Gal(E/F) is abelian. Prove that for every...
Let E/F be a finite Galois extension such that Gal(E/F) is abelian. Prove that for every intermediate field K, the extension K/F is Galois.
For any subset S ⊂ V show that span(S) is the smallest subspace of V containing...
For any subset S ⊂ V show that span(S) is the smallest subspace of V containing S. (Hint: This is asking you to prove several things. Look over the proof that U1+. . .+Um is the smallest subspace containing U1, . . . , Um.)
Let f be monotone increasing and absolutely continuous on [0, 1]. Let E be a subset...
Let f be monotone increasing and absolutely continuous on [0, 1]. Let E be a subset of [0, 1] with m∗(E) = 0. Show that m∗(f(E)) = 0. Hint: cover E with countably many intervals of small total length and consider what f does to those intervals. Use Vitali Covering Argument
For a nonempty subset S of a vector space V , define span(S) as the set...
For a nonempty subset S of a vector space V , define span(S) as the set of all linear combinations of vectors in S. (a) Prove that span(S) is a subspace of V . (b) Prove that span(S) is the intersection of all subspaces that contain S, and con- clude that span(S) is the smallest subspace containing S. Hint: let W be the intersection of all subspaces containing S and show W = span(S). (c) What is the smallest subspace...
Let F be an ordered field.  Let S be the subset [a,b) i.e, {x|a<=x<b, x element of...
Let F be an ordered field.  Let S be the subset [a,b) i.e, {x|a<=x<b, x element of F}. Prove that infimum and supremum exist or do not exist.
Let n be a positive integer and let S be a subset of n+1 elements of...
Let n be a positive integer and let S be a subset of n+1 elements of the set {1,2,3,...,2n}.Show that (a) There exist two elements of S that are relatively prime, and (b) There exist two elements of S, one of which divides the other.
Let A, B be sets and f: A -> B. For any subsets X,Y subset of...
Let A, B be sets and f: A -> B. For any subsets X,Y subset of A, X is a subset of Y iff f(x) is a subset of f(Y). Prove your answer. If the statement is false indicate an additional hypothesis the would make the statement true.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT