Modern Algebra: An Introduction - 6 Edition - Chapter 28 - Problem 28.7
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# 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:

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

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