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Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230

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Section
BuyFindarrow_forward

Elements Of Modern Algebra

8th Edition
Gilbert + 2 others
ISBN: 9781285463230
Textbook Problem

If e denotes the unity element in an integral domain D , prove that m e n e = ( m n ) e for all

m , n Z .

To determine

To prove: If e denotes the unity element in an integral domain D, mene=(mn)e for all m,n.

Explanation

Formula used:

Definition: Integral domain:

Let D be a ring. Then D is an integral domain, provided these conditions hold:

1. D is a commutative ring.

2. D has a unity e, e0.

3. D has no zero divisors.

Proof:

Let e denote the unity element in an integral domain D.

Consider mene for all m,n

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