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Abstract Algebra
Notes 4. Find the g.c.d. of
(a) 2 and 6 in Z/ 8 , (b) x + 8x + 15 and x + 12x + 35 in Z[x],
2
2
(c) x 2x + 6x 5 and x 2x + 1 in Q[x].
3
2
2
5. Let R be a PID and a, b, c R such that a (bc. Show that if (a, b) = 1, then a | c.
(Hint: By Theorem 4, x, y R such that ax + b = 1.)
Answers: Self Assessment
1. (a) 2. (a) 3. (b) 4. (c) 5. (b)
20.6 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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