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Abstract Algebra: An Introduction
Found in: Page 94
Abstract Algebra: An Introduction

Abstract Algebra: An Introduction

Book edition 3rd
Author(s) Thomas W Hungerford, David Leep
Pages 608 pages
ISBN 9781111569624

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Short Answer

Show that 1+3x is a unit in 9x . Hence, Corollary 4.5 may be false if R is not an integral domain.

It is proved that 1+3x is a unit in 9x .

See the step by step solution

Step by Step Solution

Step 1: Polynomial Arithmetic

If any given function R[x] is a ring, then the commutative, associative, and distributive laws hold such that the function f(x)+g(x) exists.

Step 2: Fields:

The given unit is 1+3x . The multiplicative inverse of this will be: 1-3x.

Then, we have:


Clearly found to be in 9x .

Hence proved, 1+3x is a unit in 9x .

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