Let E be an intermediate field. (a) If F is algebraic Galois over K, then F is

Question:

Let E be an intermediate field.

(a) If F is algebraic Galois over K, then F is algebraic Galois over E. show that the "algebraic" hypothesis is necessary.

(b) If F is Galois over E, E is Galois over K and F is a splitting field over E of a family of polynomials in K[x], then F is Galois over K.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

See More Books

Question Posted: Apr 16, 2023 03:50 AM

See More Questions

A combustion test was performed on a mixture of H and O2 in a steady flow reactor at a pressure of 20 atm. The composition of the exiting products measured in terms of the mole fractions is shown in...
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)...
(a) Let E be an intermediate field of the extension K F and assume that E = K(u 1 , ... , u r ) where the u i , are (some of the) roots of K[x]. Then F is a splitting field of over K if and only...
Pipestone Ltd. (Pipestone) uses an aging schedule to estimate the amount of receivables that won't be collected. Pipestone allows its customers up to 60 days to pay amounts owed. Any receivable...
You are analyzing Tiffanys, an upscale retailer, and find that the regression estimate of the firms beta is 0.75; the standard error for the beta estimate is 0.50. You also note that the average...
Using the income statement for Dynasty Travel Service shown in Practice Exercise 1-1A, prepare a retained earnings statement for the current year ended June 30, 2012. Nancy Coleman, the owner,...
Explain in detail how a Kohonen map might be used to cluster a set of web documents in response to a users keyword query.
The just completed year, Hanna Company had a net income of $35,000. Balances in the companys current asset and current liability accounts at the beginning and end of the year were: The Deferred...
Debt to Equity = total debt / total equity Year 2 = 316,632/146,043 Year 1 = 282,304/138,245 = 2.17 = 2.04 1. What does this ratio tell you? 2. In general, would you like this ratio to be higher or...
On 1 January 20x6, Company X acquires the entire share capital of $500,000 comprising of 500,000 ordinary shares in Company Y. Retained earnings as that date amounted to $100,000. In previous years,...
Proof that Let F be an algebraic extension of K such that every polynomial in K[x] has a root in F. Then F is an algebraic closure of K.
In the field K(x), let u = x 3 /(x + 1). Show that K(x) is a simple extension of the field K(u). What is [K(x) : K(u)]?
What benefits can flow from processing sales details on a computer?
Part of being a good systems person is reading and understanding people. Notice someone who seems a little down or is having a bad day. Do something nice for that person. It doesnt matter whether you...
Alan Energy Corporation acquired a lease with a four-year primary term, paying $350/acre. During the next three years, Alan drilled three dry holes on the property. With one more year of the primary...
In depreciating the cost of a well in accordance with the successful efforts method, which reserves should be used? a. Proved reserves b. Proven and probable reserves c. Proved developed and...
When computing DD&A for any given period, the book value is computed a. By taking the beginning of period costs less beginning of period accumulated depreciation b. By taking the end of period costs...
Write down all of the common computer/technical jargon you use when you describe a system. As a team or individually, write down a nontechnical, anybody would understand version of each of the...
If x has a normal distribution with mean = 15 and standard deviation = 3, describe the distribution of values for sample size n, where n = 4, n = 16, and n = 100. How do the x distributions compare...
What are the principal differences among asset liquidity management, liability management, and balanced liquidity management?
Answer the same question as Problem 10.32 considering 36- to 45-year-old males only? Mental Health A study was performed in Lebanon looking at the effect of widowhood on mortality [14]. Each of 151...
Implement the test in Problem 10.34, and report a p-value? Mental Health A study was performed in Lebanon looking at the effect of widowhood on mortality [14]. Each of 151 widowers and 544 widows...
Based on all matched pairs, how much power did the study just mentioned have vs. the alternative hypothesis that a widower is twice as likely to die before a married person of the same age and...
For a particular taxable year, X Corp., a DE corp., has taxable income of $ 1 , 0 0 0 ( before taking foreign income taxes into account ) , of which $ 2 0 0 is from sources outside the U . S . Assume...
Luxor Corp. had E & P of $ 3 0 , 0 0 0 . They had no additional E & P for the year. On 7 / 1 / 2 3 the corporation distributes $ 4 0 , 0 0 0 to its only shareholder, Maria. Her stock basis was $ 8 ,...
Discuss what is meant by a marketspace, its components and participants, and types. Are there winners and losers in the e - marketplace? Why, or why not? Please discuss and use real life examples to...

Let E be an intermediate field. (a) If F is algebraic Galois over K, then F is

Question:

Step by Step Answer:

a The algebraic hypothesis is necessary Suppose that F is algebraic Galois over K but not algebraic Galois over E This means that there exists an elem...View the full answer

Algebra Graduate Texts In Mathematics 73

Students also viewed these Mathematics questions