Page 202 - DMTH403_ABSTRACT_ALGEBRA

Unit 19: The Field of Quotient Euclidean Domains

3. Find all the units in Notes
(a) Z (b) Z (c) Z/5Z (d) Z + IZ
6
4. Let R be an integral domain. Show that
(a) u is a unit in R iff u | 1.
(b) for a, b  R, a | b and b | a iff a and b are associates in R.
5. Which of the following polynomials is irreducible? Give reasons for your choice.

(a) x – 2x + 1  R[x] (b) x + x + 1  C[x]
2
2
(c) x – i  C[x] (d) x – 3x + 2x + 5  R[x].
3
2
Answers: Self Assessment
1. (a) 2. (c) 3. (a) 4. (c) 5. (b)

19.6 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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