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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
find and simplify the difference quotient for fx square root of
During the meeting, several employees remark that some of the clients have asked advice about offering a trade discount for purchases in wholesale quantities.
In an exponential smoothing model, if the smoothing constant (alpha) were equal to 0, then. The forecast would never change.
business rate schedulea utility company has the following rate schedule for natural gas usage in a citys business
Problems on probability
The slope of the line.
Determine the corresponding z -transform G(z) and the characteristic equation for this system. Using the bilinear transformation and Routh's Stability Criterion, determine the range of K for stability when the sampling time T = 0.25 s.
patricia had less than 9 to spend when she went to the grocery store. she bought 1 pound of tomatoes and wanted to
explain the five-steps for solving rational equations. can any of these steps be eliminated? can the order of these
Find the remainder and quotient
Use the substitution method to determine whether the system of equations has one solution, no solutions or infinitely many solutions.
State the domain of the following.
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