(a) K is a perfect field if and only if every field extension of K is separable....

Question:

(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.

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 20, 2023 03:00 AM

See More 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)...
Mark each of the following true or false. _______ a. Every finite extension of every field F is separable over F. _______ b. Every finite extension of every finite field F is separable over F....
KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...
Which description does NOT fit in description of "issues" in the context of international standards? a. An unsettled matter. b. A vital matter. c. A change in the environment. d. A concern or...
List at least three tests that could be performed to detect falsified hours and salary schemes.
A company purchased machinery for $10,800,000 on January 1, 2013. The machinery has a useful life of 10 years and an estimated salvage value of $800,000. What is the depreciation expense on the...
Which financial statement analysis measure provides information concerning the sales output that a firms assets produce? LO.1
Strategic analysis of operating income (continuation of 13-26). Refer to Exercise 13-26. 1. Calculate the operating income of Snyder Corporation in 2008 and 2009. 2. Calculate the growth,...
ow.com/ilm/take Assignment/take Assignment Main do Pinprogress true eBook Multiple-step income statement and balance sheet The following selected accounts and their current balances appear in the...
For the spring assemblages shown in Figures P2-8 through P2-16, determine the nodal displacements, the forces in each element, and the reactions. Use the direct stiffness method for all problems....
Let char K = p 0 and let u be transcendental over K. Suppose F is generated over K by {u,v 1 ,v 2 , ... } , where v i is a root of x pi - u K(u)[x] for i = 1,2, .... Then F is separable over K, but...
Romero, Inc., had a $60,000 balance in its Accounts Payable account at the beginning of the year. By year-end this balance had increased by $10,000. During the year, Romero made $630,000 of...
The notes to recent financial statements of Xerox Corporation disclosed the following tabular information regarding restructuring charges. (Assume all restructuring charges were for employee...
Gil and Ruth George have been friends of yours for many years. They have come to you for advice on their estate plan since they want a second opinion to make sure it is going to do what they hope....
The test statistic of z = 1.74 is obtained when testing the claim that p # 0.658. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. Find the P-value. Using a...
Ann and Bob had their first date. Each either felt romantic chemistry (C) or no chemistry (NC) with the other person. Each person knows his/her own feeling but does not know the feeling of the other...
Find the following using countif, countifs, sumif, sumifs, averageif, and averageifs. Create all formulas and calculations directing in Excel. How many songs are sung by Moore? What is the average...
Total number of Ledgers, Groups, Entries etc. can be shown from o a. Tally Audit o b. Statistics o c. Accounts Information o d. Company Information
Sue, of Sues Sandwich Shoppe, sells sandwiches and sodas from a sidewalk cart in a popular park near her house. She sets up her cart in the summers to earn money for college tuition. Last month she...
1. What is the semi-annually compounded interest rate if $200 accumulates to $318.77 in eight years? Answer in percentage with two decimal places. 2. What is the quarterly compounded interest rate if...
What does the variable Î² 1 mean in the 2nd logistic regression (Table 13.63)? How does it differ from the meaning of Î² 1 in the 1st logistic regression (Table 13.62)? Two...
Estimate the OR for the association between age at menarche and ovarian cancer after controlling for race, and provide a 95% CI about this estimate? Two logistic models were run with Stata Version 11...
For both Caucasians and African Americans (seperately), estimate the OR between late age at menarche (¥12) and ovarian cancer risk and provide a 95% CI about these estimate? Cancer Results from a...
ACC 2 0 2 Milestone One: Operational Costs Data Appendix You plan to open a small business for manufacturing pet collars, leashes, and harnesses. You have found a workshop space you can use for...
Explain the following: Understand the PPE acquisition (or investing) cycle and related significant transactions and source documents Understand the relevant assertions/objectives about PPE balances...
Problem 3 Progress Company acquired 6 0 % of Stall Corporation on 1 2 0 2 0 . Fair values of Stall's assets and liabilities approximated book values on that date. Progress uses the initial value...

(a) K is a perfect field if and only if every field extension of K is separable....

Question:

Step by Step Answer:

a To prove that K is a perfect field if and only if every field extension of K is separable we need ...View the full answer

Algebra Graduate Texts In Mathematics 73

Students also viewed these Mathematics questions