Proof that Let F be algebraic over K. F is normal over K if and only if
Question:
Proof that Let F be algebraic over K. F is normal over K if and only if for every K-monomorphism of fields σ : F → N, where N is any normal extension of K containing F, σ(F) = F so that σ is a K-automorphism of F.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 85% (7 reviews)
To prove the statement Let F be algebraic over K F is normal over K if and only if for every Kmonomorphism of fields F N where N is any normal extensi...View the full answer
Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
Question Posted:
Students also viewed these Mathematics questions
-
Proof that Let F be a splitting field of K[x]. Without using Theorem 3.14 show that F is normal over K. Data from theorem 3.14 lf F is an algebraic extension field of K, then the following...
-
Let F be an algebraic closure of the field Q of rational numbers and let E F be a splitting field over Q of the set S = { x 2 + a | a Q} so that E is algebraic and Galois over Q (Theorem 3.11). (a)...
-
Part (ii) or (ii)' of the Fundamental Theorem (2.5) is equivalent to: an intermediate field E is normal over K if and only if the corresponding subgroup E' is normal in G = Aut K F in which case G i...
-
How might a shareholders agreement influence a companys financial report-ing objectives?
-
You have a project that does not require an initial investment but has its expenses spread over the life of the project. Can the IRR be estimated for this project? Why or why not?
-
You have been asked to prepare a December cash budget for Ashton Company, a distributor of exercise equipment. The following information is available about the company s operations: The cash balance...
-
A lossless motor drives the fan shown in Fig. P12.40 at \(40 \mathrm{~Hz}\). The power input to the motor is \(40 \mathrm{amps}\) at 440 volts. For the geometry shown, what is the discharge flow rate...
-
Sven's Cookhouse is a popular restaurant located on Lake Union in Seattle. The owner of the restaurant has been trying to better understand costs at the restaurant and has hired a student intern to...
-
1. Referring to the diagram, if the velocity of B is constant at 1.5 m/s upward, determine the angular velocity of the rod AB in rad/s. (use three decimal places)2. Find the velocity of point A along...
-
The adjusted trial balance for Tybalt Construction on December 31 of the current year follows. The Retained Earnings account balance was $111,400 on December 31 of the prior year. Required 1. Prepare...
-
Show that F is an algebraic extension of K if and only if for every intermediate field E every monomorphism u : E E which is the identity on K is in fact an automorphism of E.
-
(a) Let L and M be intermediate fields of the extension K F, of finite dimension over K. Assume that [LM : K] = [L : K][M : K] and prove that L M = K. (b) The converse of (a) holds if [L : K] or [M...
-
The three vibrational frequencies in H 2 O (1595, 3657, and 3756 cm 1 ) are all much larger than the corresponding frequencies in D 2 O (1178, 2671, and 2788 cm 1 ). This follows from the fact that...
-
1. Do you think women are more apt to seek professional help for their mental disorders than men? Why? 2. Would you agree that depression among men is often masked by drinking or drug problems? 3. Do...
-
How do the local electronic and printing advertisements apply in the real ground? What are the most accepted brand names? What are the good qualities and demerits of the brand?
-
What are the four principle modes for moving people Which of these modes accounts for the largest share of passenger - miles? Which mode accounts for the lowest?
-
Which management thinker has given the following definition of management: 'The use of people and other resources to accomplish objectives ?
-
What ethical considerations arise in the pursuit of scientific innovation and technological progress, and how can ethical frameworks adapt to address emerging ethical challenges?
-
Any time we conduct a survey, we must take care to avoid undercoverage. Suppose we plan to select 500 names from the city phone book, call their homes between noon and 4 P.M., and interview whoever...
-
A firm offers two products for sale. The marginal cost of one product is new zero once the first unit has been produced. The marginal cost of the other product rises as output rises. What would be...
-
Answer Problem 10.1 if compliance is as given in Example 10.37? Cardiovascular Disease Consider the Physicians Health Study data presented in Example 10.37 (p. 411).
-
How many participants need to be enrolled in each group to have a 90% chance of detecting a significant difference using a two-sided test with = .05 if compliance is perfect? Cardiovascular Disease...
-
What is your overall conclusion from your analysis of the data? Hypertension Plasma aldosterone has been related to blood-pressure levels in adults in some studies. In addition, there may be ethnic...
-
During Year 1, Starnes Corporation developed a patent. Starnes incurred the following costs related to the development of the patent tests to perfect the use of the patent for production processes,...
-
Pre-consolidation bookkeeping, upstream intercompany sales, profits in ending inventory-Equity method Assume that a parent company owns a 100% controlling interest in its long-held subsidiary. The...
-
to mail an envelope first class the U.S. post office charges 40 cents for the first ounce and 25 cents per ounce for each additional ounce. Use an inequality to find the number f whole ounces that...
Study smarter with the SolutionInn App