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Modern Algebra: An Introduction | 6th Edition | ISBN: 9780470384435 | Authors: John R. Durbin
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Throughout this set of problems D denotes an ordered integral domain. Prove that if a

Chapter 28, Problem 28.4

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QUESTION:

Throughout this set of problems D denotes an ordered integral domain. Prove that if a, bED, and a < and b < 0, then ab > O.

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QUESTION:

Throughout this set of problems D denotes an ordered integral domain. Prove that if a, bED, and a < and b < 0, then ab > O.

ANSWER:

Step 1 of 4

Definition?1: An integral domain D is said to be ordered if there is a subset of D such that:

(i) Closure under addition: If , then 

(ii) Closure under multiplication: If , then

(iii) Law of trichotomy: If , then exactly one of the following is true, or

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 that b is less than a

 

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