Show that F is an algebraic extension of K if and only if for every intermediate field

Question:

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.

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

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...
Proof that F is an algebraic closure of K if and only if F is algebraic over K and for every algebraic field extension E of another field K 1 and isomorphism of fields : K 1 K, extends to a...
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...
Prepare a sensitivity analysis question with an Excel Sensitivity analysis report and answer it. Make sure your question asks about the following a. Optimal solution b. Optimal objective function c....
Businesses with severe capital rationing constraints should use IRR more than NPV. Do you agree? Explain.
The productions supervisor of the Machining department for Cramer Company agreed to the following monthly static budget for the up coming year: Cramer Company Machining Department Monthly Production...
Explain how a system might be built that could reproduce itself. Would such a system be alive?
The Farm-4-Less Tractor Company produces a grain combine (GC) in addition to both a large (LT) and small size tractor (SM). Its production manager desires to produce to customer demand using a mixed...
At first July 2018 creative Limited acquired 150,000 shares in brokerage Limited at a price of five dollars each. There were brokerage fees of $1000. The closing market price on brokerage Limited...
If the resultant force acting on the bracket is FR = {? 300i + 650j + 250k} N, determine the magnitude and coordinate direction angles of F. 45 30- F= 750 N
Proof that If F is algebraic over K and every element of F belongs to an intermediate field that is normal over K, then F is normal over K.
Proof that Let F be algebraic over K. F is normal over K if and only if for every K-monomorphism of fields : F N, where N is any normal extension of K containing F, (F) = F so that is a...
Show that if |a 5| < 12 and |b 8| < 12, then|(a + b) 13| < 1. Use the triangle inequality (|a + b| |a| + |b|).
Repeat the fractal pattern form a star with several colors. Begin with five lines (see Fig. 18.22 ) instead of one, where each line is a different arm of the star. Apply the Lo feather fractal...
Which of the following costs would always be charged to expense under the full cost method? (Choose all that apply.) a. Exploratory dry holes b. Salary and benefits of a company geologist c. Salary...
When is a ceiling test write-down required? a. When the ceiling exceeds the total net capitalized costs b. When the total net capitalized costs exceeds the present value of future net revenues from...
Compute the variance-covariance matrix for the 10 stocks. Using the monthly average returns and a monthly risk-free interest rate of 0.20%, compute an efficient portfolio. Here?s the template: DIE F...
When would the surrender or abandonment of an unproved property result in recognition of a loss? a. Loss is recognized any time an individually significant unproved property is abandoned. b. Loss is...
A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches and the standard deviation is 2 inches. A random sample of...
Design a circuit which negative the content of any register and store it in the same register.
Answer Problem 10.4 if compliance is as given in Example 10.37. Refer to Table 2.13 (p. 36). Table 2.13: Hospital-stay data
Suppose 11,000 men are actually enrolled in each treatment group. What would be the power of such a study if a two-sided test with = .05 were used and compliance is perfect? Cardiovascular Disease...
Answer Problem 10.1 if a one-sided test with power = .8 is used and compliance is perfect? Cardiovascular Disease Consider the Physicians Health Study data presented in Example 10.37 (p. 411).
During 2021, Albert redeems Series EE savings bonds for $6,000 - - consisting of $2,000 interest and $4,000 principal. Albert has net qualifying education expenses of $5,000 in 2021. Albert, a single...
= 2. (a): XYZ Inc. just paid out a dividend (Do) of $4.50. The firm anticipates that its annual dividends will grow at g 15% a year over the next 5 years. From t=5 onwards, the management expects...
Elon Musk decided to take over Twitter. Twitter has 50 million stocks outstanding with a current price of $40 per share. On 1/07/2022 Musk offered $48 per share conditioned on buying at least 50% of...

Show that F is an algebraic extension of K if and only if for every intermediate field

Question:

Step by Step Answer:

We will prove the statement in two parts Part 1 If F is an algebraic extension of K then for every i...View the full answer

Algebra Graduate Texts In Mathematics 73

Students also viewed these Mathematics questions