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Q11.

Expert-verified

Abstract Algebra: An Introduction

Found in: Page 134

Book edition 3rd

Author(s) Thomas W Hungerford, David Leep

Pages 608 pages

ISBN 9781111569624

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Short Answer

Show that the ring in Exercise 8 is not a field.

There is no inverse for element [x].

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Determine function ring is not field

Consider the ring in that there is no inverse for the element [x]. Now assume $[a_{0} + a_{1} x]$ is an inverse. That means

$[x] \cdot [a_{0} + a_{1} x] = [a_{0} x] = [1]$

It is a contradiction as there is no $a_{0} \in ℚ$ , so that $x^{2}| a_{0} x - 1$ .

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