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Abstract Algebra
Notes 23.4 Review Questions
1. Express f as gq + r, where deg r < degg, in each of the following cases.
(a) f = x + 1, g = x in Q[x]
3
4
3
(b) f = x + 2x x + 1, g = x + 1 in Z [x].
2
3
(c) f = x 1, g = x 1 in R[x].
3
p
2. You know that if p, q Z, q 0, then can be written as the sum of an integer and a
q
fraction * with | m | < | q |. What is the analogous property for elements of F[x]?
Answers: Self Assessment
1. (a) 2. (a) 3. (a) 4. (a)
23.5 Further Readings
Books Dan Saracino: Abstract Algebra; A First Course.
Mitchell and Mitchell: An Introduction to Abstract Algebra.
John B. Fraleigh: An Introduction to Abstract Algebra (Relevant Portion).
Online links www.jmilne.org/math/CourseNotes/
www.math.niu.edu
www.maths.tcd.ie/
archives.math.utk.edu
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