Let char K = p 0 and let u be transcendental over K. Suppose F is
Question:
Let char K = p ≠ 0 and let u be transcendental over K. Suppose F is generated over K by {u,v1,v2, ... } , where vi is a root of xpi - u ϵ K(u)[x] for i = 1,2, .... Then F is separable over K, but F is not separably generated over K.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 50% (8 reviews)
Let me explain the given description in detail Given K is a field with characteristic K 0 u is a tra...View the full answer
Answered By
Rodrigo Louie Rey
I started tutoring in college and have been doing it for about eight years now. I enjoy it because I love to help others learn and expand their understanding of the world. I thoroughly enjoy the "ah-ha" moments that my students have. Interests I enjoy hiking, kayaking, and spending time with my family and friends. Ideal Study Location I prefer to tutor in a quiet place so that my students can focus on what they are learning.
5.00+
1+ Reviews
10+ Question Solved
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
-
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)...
-
In annual report, WRM Athletic Supply, Inc. includes the following five-year financial summary: Analyze the companys financial summary for the fiscal years 2016-2020 to decide whether to invest in...
-
Suppose you own a business that does well during economic expansions but not so well during recessions which happen with probability . Let xE denote your consumption level during expansions and let...
-
Why is it important to have a defined project scope? Why is it important to make sure there is agreement about the scope? Is there anything in the "Why Should You Use the WBS?
-
There are two ways that an employee working on commission can fraudulently increase his pay. What are they?
-
When a double bond has two identical groups (one on each vinylic position), we can use either cis-trans terminology or E-Z terminology: The configuration of this double bond can be designated as...
-
Benchmarking of eco-efficiency indicators faces a number of practical problems. What are these? Can they be overcome? Why is internal benchmarking more common than external benchmarking?
-
An investor purchases a stock for $38 and a put for $.50 with a strike price of $35. The investor sells a call for $.50 with a strike price of $40. What is the maximum profit and loss for this...
-
Consider a standing normal shock in a steady one-dimensional ow from left to right. Sketch, on an x-t diagram, the shock itself, particle paths and both families of characteristics in the...
-
Where are the current career opportunities for the IT auditor? Search the Internet and identify at least one job profile/description for each career opportunity identified above. For each job profile...
-
Proof that If F is algebraically closed and tr.d.F/K is finite, then every K-monomorphism F F is in fact an automorphism.
-
(a) K is a perfect field if and only if every field extension of K is separable. (b) (Mac Lane) Assume K is a perfect field, F is not perfect and tr.d.F/ K = 1. Then F is separably generated over K.
-
The following transactions of Philadelphia Pharmacies occurred during 2023 and 2024: Journalize the transactions in Philadelphias general journal. Explanations are not required. 2023 Jan. 9 29 Feb. 5...
-
This problem is based on the Hansen and King (1996) data set and the replication by McCoskey and Selden (1998). Hansen and King (1996) studied the stationarity properties of real per capita health...
-
Euro Classics Ltd has been operating a successful business for many years specialising in servicing and reconditioning repairs for classic European automobiles. Servicing costs $750, while...
-
What is the solubility of oxygen in methanol at 25C and 1 bar? What is the solubility of oxygen in methanol at 25C and 100 bar? Take Vo = 4.5 10-5 [m/mol].
-
A watermelon is taken out of the refrigerator at a uniform temperature of \(3^{\circ} \mathrm{C}\) and is exposed to \(32^{\circ} \mathrm{C}\) air. Assume that the watermelon can be approximated as a...
-
You have come up with a great idea for a Sawasdee Thai restaurant. After doing a financial analysis of this venture, you estimate that the initial outlay will be \($5\) million. You estimate that...
-
When defining a target audience for communications, why is it a good idea to use consumer behavior with respect to your brand as the primary variable before using variables such as demographics or...
-
Determine by direct integration the values of x for the two volumes obtained by passing a vertical cutting plane through the given shape of Fig. 5.21. The cutting plane is parallel to the base of the...
-
Use ordinal logistic regression to assess the association between SBP z-score group and the same variables in Problem 13.122? Hypertension The data set WALES.DAT contains familial data on blood...
-
13.122 Use polytomous logistic regression with group = 0 as the reference group to assess the association between SBP z-score group and the following variables: (a) BMI, (b) height, (c) region (i.e.,...
-
Assess whether the effect of age at menarche is different for Caucasian vs. African American women. Report a p-value (two-tailed)? Two logistic models were run with Stata Version 11 using these data....
-
Anais, a math teacher, noticed that the average grade, G, on an exam given that n students - watch the related video can be given by the function G(n) = 50+ 1.5n. She also noticed that the number, S,...
-
The balance sheet for Quinn Corporation is shown here in market value terms. There are 26,000 shares of stock outstanding. Market Value Balance Sheet Cash Fixed assets Total $ 136,000 544,940 $...
-
Assume the following sales data for a company: Current year Preceding year $780,051 587,071 What is the percentage increase in sales from the preceding year to the current year?
Study smarter with the SolutionInn App