Let p be a prime. Let L be a Galois extension of K with [L : K] = p^n. For both m = p and m = p^(n-1), show there is a normal extension of K of degree m contained in L.
Show that Ann(σ) is the augmentation ideal, the kernel of φ: R → A defined by φ(g) = 1
Please see attached file and please answer both questions. Thanks in advance!
Inequalities : When do you flip the inequality sign?
1.The inequality sign changes when both sides are multiplied by a negative number. This happens because it needs to read true. If you do not flip the sign it will not be a true inequality. However, if you multiply by a positive number you do not need to change the inequality sign. You do not change the sign in regular equations. ...continues
Show that the algebraic closure of Q (rational numbers) in C (complex numbers) (and hence any algebraic closure of Q, once we have the uniqueness statement) is countable.
Suppose that L has transcendence degree n over K and that L is algebraic over K(α1, . . . , αn). Show that α1, . . . , αn is a transcendence basis for L over K. Might help: Theorem – Definition: Let L be an extension of K, A a subset of L. The following are equivalent: (1) A is a maximal algebraically ...continues
Algebra and Variable Problem Solving Questions
Need solution to attach problems do not understand. Thank you,
Business Math : Price Index, Dara Analysis, Return on Investment (ROI), Inventory and Expenses
12. Key Question The following table shows nominal GDP and an appropriate price index for a group of selected years. Compute real GDP. Indicate in each calculation whether you are inflating or deflating the nominal GDP data. Year Nominal GDP Billions, Price Index (1996 = 100) Real GDP, Billions 1960 $ 527.4 22.19 $____ 19 ...continues
Chapter: 1, exercise 18 18. Refer to the Wage data, which reports information on annual wages for a sample of 100workers. Also included are variables relating to industry, years of education, and gender for each worker. a. Which of the 12 variables are qualitative and which are quantitative? b. Determine the level of me ...continues
Marriage penalty eliminated ...
Marriage penalty eliminated. The value of the expression 4220 + 0.25(x - 30,650)is the 2006 federal income tax for a single taxpayer with taxable income of x dollars, where x is over $30,650 but not over $74,200. a) Simplify the expression. b) Find the amount of tax for a single taxpayer with taxable income of $40,000. c) W ...continues
Please see the attached file for the fully formatted problems. F1 + F3 + ..................+F2n-1 = F2n
