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1.a. show that every subfield of complex numbers contains rational numbers
b. show that the prime field of real numbers is rational numbers
c. show that the prime field of complex numbers is rational numbers
2.a. Let R be a domain. Prove that the polynomial f(x) is a unit in R[x] if and only if f(x) is a nonzero constant which is a unit in R.
b. Show that ([2]x + [1])^2 = [1] in (integers modulo 4)[x] Conclude that the statement in part (a) may be false for the commutative rings that are not domains. [ An element z element of R is called a nilpoint if z^m = 0 for some integer m greater than or equal to one. For any commutative ring R, it can be proved that a polynomial f(x) = a(sub 0) + a(sub 1)x +...+a(sub n)x^n element R[x] is a unit in R[x] if and only if a(sub 0) is a unit in R and a(sub i) is nilpoint for all I greater than or equal to 1.]
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the given line - Write an equation in slope-intercept form of the line.
pete smith found in his attic a woody woodpecker watch in its original box. it had a price tag on it for 4.40. the
After the bake sale, the Campus Ministry volunteers counted how much money they raised. In addition to the 18 one - dollar bills, the group had $9.50 in quarters, dimes, and nickels.
Find the exact value of tan (α - β), cos 2α, and sin β/2 under the given conditions: cos α =√5/5, 0
Find an orthogonal basis
Using the straight-line method, depreciation expense for 2007 and the equipment book value at December 31, 2007 would be:
Verify the inverse relationship using composition
Give the dimensions of the matrix.
The St. Marks community bbq served 250 dinners. a child's plate cost 3.50 and an adult's plate cost 7.00. A total of 1347.50 was collected. how many of each type of plate was served?
Explain your strategy for solving the problem and present a step-by-step solution of the problem.
what is the expression in index forum for the following questions
Suppose further that every $100 billion spent on defense increased taxpayer satisfaction by 5% while every $100 billion spent on other services increased satisfaction by 3%.
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