- Let R be an integral domain, which is a subring of a field F. Let F' : {ab-¹ | a,b € R, b# 0}. Show that F' is a subfield of F. Furthermore, show that F' is the smallest subfield of F which contains R.

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Embedding of Rings 

Let R be an integral domain, which is a subring of a field F. Let F'
{ab-¹ | a,b € R, b 0}. Show that F' is a subfield of F. Furthermore,
show that F' is the smallest subfield of F which contains R.
Transcribed Image Text:Let R be an integral domain, which is a subring of a field F. Let F' {ab-¹ | a,b € R, b 0}. Show that F' is a subfield of F. Furthermore, show that F' is the smallest subfield of F which contains R.
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