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Modern Algebra: An Introduction | 6th Edition | ISBN: 9780470384435 | Authors: John R. Durbin
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For D an ordered integral domain, let Dn denote the set of all nonzero elements not in

Chapter 29, Problem 29.5

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QUESTION:

For D an ordered integral domain, let Dn denote the set of all nonzero elements not in DPProve that if D is well ordered, then every nonempty subset S of D" has a greatest element'that is, an element b E S such that x< b for each XES such that x =I b.

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QUESTION:

For D an ordered integral domain, let Dn denote the set of all nonzero elements not in DPProve that if D is well ordered, then every nonempty subset S of D" has a greatest element'that is, an element b E S such that x< b for each XES such that x =I b.

ANSWER:

Step 1 of 2

We know that integral domain D is well ordered if every non empty subset of has the least element.

Now, D is well ordered.

 must have the greatest element.

It is clear that denotes the set of all non-zero elements not present in.

Let us assume that  has no greatest element.

 

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