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Solutions for Modern Algebra: An Introduction | 6th Edition | ISBN: 9780470384435 | Authors: John R. Durbin 9780470384435

Solution for problem 28.7 Chapter 28

Complete the proof of Theorem 28.2

Modern Algebra: An Introduction | 6th Edition


Problem 28.7

Complete the proof of Theorem 28.2.

Accepted Solution
Step-by-Step Solution:

Step 1 of 9

Definition-1:

An integral domain D is said to be ordered if there is a subset  of D such that:

Closure under addition:

If  then

Closure under multiplication:

If  then

Law of trichotomy:

If , then exactly one of the following is true:

Note: The elements of  are called the positive elements of D.

Definition-2:

Assume that D is an ordered integral domain and. Then  will mean that.

If, we say that a is greater than b and b is less than a.

Lemm-1: If  and , then  

 

Chapter 28, Problem 28.7 is Solved

Step 2 of 9


Step 3 of 9

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Complete the proof of Theorem 28.2