A (possibly infinite) algebraic extension E of a field F is a separable extension of F if
Question:
A (possibly infinite) algebraic extension E of a field F is a separable extension of F if for every α ∈ E, F(α)
is a separable extension of F, in the sense defined in the text. Show that if E is a (possibly infinite) separable
extension of F and K is a (possibly infinite) separable extension of E, then K is a separable extension of F.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 41% (12 reviews)
Because K is algebraic over E and E is algebraic over F we have K algebraic over F by Exercise 31 of ...View the full answer
Answered By
Joseph Ogoma
I have been working as a tutor for the last five years. I always help students to learn and understand concepts that appears challenging to them. I am always available 24/7 and I am a flexible person with the ability to handle a wide range of subjects.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
A finite normal extension K of a field F is cyclic over F if G(K/F) is a cyclic group. a. Show that if K is cyclic over F and E is a normal extension of F, where F E K, then E is cyclic over F and...
-
A finite normal extension K of a field F is abelian over F if G(K/F) is an abelian group. Show that if K is abelian over F and p is a normal extension of F, where F E K, then K is abelian over E...
-
Show that if E is an algebraic extension of a field F and contains all zeros in F of every f(x) F[x]. then E is an algebraically closed field.
-
Suppose a product can be produced using virgin ore at a marginal cost given by MC 1 = 0. 5q 1 and with recycled materials at a marginal cost given by MC 2 = 5 + 0. 1q 2 . (a) If the inverse demand...
-
What is the relationship between the accounting cycle and the worksheet?
-
How can learning to manage chaos better prepare supervisors for their jobs in the next decade?
-
Dairymaid makes organic yogurt. The only ingredients, milk and bacteria cultures, are added at the very beginning of the fermentation process. At month end, Dairymaid has 100,000 cups of yogurt that...
-
Apex Fitness Club uses straight- line depreciation for a machine costing $ 23,860, with an estimated four-year life and a $ 2,400 salvage value . At the beginning of the third year, Apex determines...
-
12.Indicate, by clicking on the relevant boxes, whether the following statements are true or false?
-
Prove that the algebraic closure of Q() in C is isomorphic to any algebraic closure of Q(x), where Q is the field of algebraic numbers and x is an indeterminate.
-
Let F E F where F is an algebraic closure of a field F. The field E is a splitting field over F if and only if E contains all the zeros in F of every polynomial in F[x] that has a zero in E.
-
Millie Abrams opened a ceramic studio in leased retail space, paying the first months rent of $300 and a $1,000 security deposit with a check on her personal account. She took molds and paint, worth...
-
We have five boxes: two boxes contain two white marbles and one black marble each, one box contains ten black marbles, two boxes contain three white marbles and one black marble each. We draw a box...
-
The following are the facts of this Hair Spray, Inc. Expected growth rate for the next 3 years 32.00% Expected growth rate thereafter (after 3 years) 7.20% Hair Spray Inc. required return 14.00% $...
-
can you please help me do a IS/BS for below company... James North, managing director and sole shareholder of Top Tier Manufacturing (Pty) Ltd has approached you for some financial help. The...
-
Complete the table given below Bridgeport Bridgeport started his own consulting firm, Bridgeport Consulting, on June 1, 2022. The trial balance at June 30 is as follows. Cash BRIDGEPORT...
-
Assume that: Crew 1 measured A to B Crew 2 measured B to C Crew 3 measured C to D A B Distances A to B (measured 4 times): 99.96, 100.01, 100.00, 100.02 Distances B to C (measured 5 times): 99.98,...
-
Describe the steps a land surveyor would need to do when performing a boundary survey.
-
Using the theoretical sampling strategy, how many samples of size 4 (n = 4) can be drawn from a population of size: (a) N = 5? (b) N = 8? (c) N = 16? (d) N = 50?
-
If there are influential points or outliers in your data, why is it a good idea to run the analysis with those points removed?
-
For the data in each of the following scatterplots, are the validity conditions met to run a theory-based test for regression? If the answer is no on any of them, explain why not. a. b. c. d. 100 90...
-
A regression table is shown based on data used to test an association between the amount of sleep someone had the previous night (in hours) and the time needed to complete a paper and pencil maze (in...
-
11. The current in a metallic conductor is plotted against voltage at two different temperatures T and T2. Which is correct :- Current 2 (1) T Voltage (2) T
-
6. A dipole is placed in uniform electric field such that potential energy of dipole is maximum (U). The work done in rotating a dipole by 180 is :- (1) U (3) -2U (2) 3U (4) -U 7. Electric charges q,...
-
15. If y = 3x-4x+2 then slope at x = 1 is: (1) 1 (2) 2 (3) 4 (4) -2 16. sin240 = ? (1) - 2 (3) 3 1/2 17. Value of sin 2 is (4) (2) 12 (1) 23 (2) (3) 90 180 (4) 0 18. The rate of mass of the gas...
Study smarter with the SolutionInn App