nov11 - s / ( pq )+ R ) = ( r + R ) ( s / ( pq )+ R ) = ( s...

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Math 5125 Friday, November 11 November 11, Ungraded Homework Exercise 10.4.6 on page 375 If R is any integral domain with quotient field Q , prove that ( Q / R ) R ( Q / R ) = 0. The general element of ( Q / R ) is of the form r / p + R , where p , r R and p 6 = 0. Now for q , s R with q 6 = 0, we have ( r / p + R ) ( s / q + R ) = ( r / p + R ) p ( s / ( pq )+ R ) = p ( r / p + R ) (
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Unformatted text preview: s / ( pq )+ R ) = ( r + R ) ( s / ( pq )+ R ) = ( s / ( pq )+ R ) = . Since every element of ( Q / R ) R ( Q / R ) is a sum of simple tensors u v , it follows that ( Q / R ) R ( Q / R ) = 0....
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This note was uploaded on 01/02/2012 for the course MATH 5125 taught by Professor Palinnell during the Fall '07 term at Virginia Tech.

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