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1. If E, F are fields and F is a subring of E, show each q in Aut(E/F) permutes the roots in E of each nonzero p(x) in F[x]. Hint if p(x)=a0+a1x+a2x^2+. . . +anx^n then p(x) has at most n roots in E. show that for z in E, p(z)=0 implies p(q(z))=0
2 If R is a commutative ring of prime characteristic p, show the function f:R-->R, f(r)=r^p is a ring homomorphism
3. If a,b are positive integers with greatest common divisor d and least common multiple m, show aZ+bZ=dZ and aZ intersect bZ=mZ
4. For the cyclic group (Z,+) = <1> prove the ideal of Z is principal
an environmental agency worries that many cars may be violating clean air emissions standards. the agency hopes to
Create a proof by mathematical induction that demonstrates that the sum of the first n even numbers is equal to n(n + 1)
How would you express the zeros of the equation x2 - 2 = 0 ? Are the two zeros of this equation integers, rational numbers, or irrational numbers?
Apply the echelon method to solve the equation
These are two examples, one specific, and one more general, where you are given y as a function of x, and we want to find what x is in terms of y, so we want to make x the subject of the equation.
Marisol needed to borrow $2,000 to pay off a high-interest credit card debt. Her local bank offered her a simple interest $2,000 loan with a 9-month term and told her she would pay $157.50 in interest. Calculate the annual interest rate Marisol is..
Find the variation constant and write a formula that expresses teh indicated variation. c varies inversely as d and c=5 when d=2.
Compute an equation for the circle
I had asked about this question before and was supplied a graph but I can not get the problem to work out that meets the graph. Please work and demonstrate steps to arrive at the solution, identifying what points are plotted.
Plot the points and determine the slope of the line containing them. Graph Line. (-3,-7) (2,-7). For the intercepts and use them to graph equation 6x+2y=12.
In 2009, a diabetic express company charged $39.95 for a vial of type A insulin and $30.34 for a vial of type B insulin. If a total of $1747.64 was collected for 50 vials of insulin, how many vials of each type were sold?
which of the following expressions allows for the use of the power division formula in order for it to be simplified?ka
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