To prove: D^+ subseteq Q^+ Given information: text{Each} x in D text{is identified with} [x,e] text{in Q}

Sinead Mcgee 2020-11-27 Answered
To prove: D+Q+
Given information:
Each x D is identified with [x,e]in Q
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Expert Answer

sovienesY
Answered 2020-11-28 Author has 89 answers

Formula used:
1) An ordered field is an ordered integral domain that is also a field.
2) In the quotient field Q of an ordered integral domain D, defined Q+ by
Q+={[a,b]abD+}
3) Well-ordered D+:
If D is an ordered integral domain in which the set D+ of positive elements is well-ordered, then e is the least element of D+.
Proof:
Let xD+,then xD
So,[x,e]in Q where e is the least element of D+
Now eD+and xD+implies that xeD+
Therefore, [x,e]Q+Q
So, xQ+
Hence,D+Q+

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