Page 159 - DMTH403_ABSTRACT_ALGEBRA

Abstract Algebra

Notes 5. Why is ((X), , ) not a ring?
6. Show that { 0 } is a ring with respect to the usual addition and multiplication. (This is called
the trivial ring.)

7. Prove that the only ring R in which the two operations are equal (i.e., a + b = ab  a,
b  R) is the trivial ring.

   x x 

8. Show that the set of matrices   x R  is a commutative ring with unity.

   x x   
9. Let R be a Boolean ring (i.e., a = a  a  R). Show that a = –a  a  R. Hence show that R
2
must be commutative.
Answers: Self Assessment

1. (b) 2. (a) 3. (c) 4. (a) 5. (a)

14.7 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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