## Solution for problem 28.7 Chapter 28

# Complete the proof of Theorem 28.2

Modern Algebra: An Introduction | 6th Edition

Complete the proof of Theorem 28.2.

**Accepted 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