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Unit 22: Polynomial Rings
2. Calculate Notes
(a) (2 + 3x2 + 4x3) + (5x + x3) in Z[x]. (b) (6 2x ) (1 2x 5x ) in Z [x].
2
3
7
(c) (1 + x) (1 + 2x + x ) in Z[x]. (d) (1 x) (1 2x x ) in Z [x]
2
2
3
(e) (2 + x + x ) (5x + x ) in Z[x]
3
2
3. If R is a ring such that R[x] is commutative and has identity, then
(a) is R commutative?
(b) does R have identity?
Answers: Self Assessment
1. (a) 2. (a) 3. (b) 4. (a) 5. (b)
22.6 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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