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Unformatted text preview: ideal in Z (c.f. section I.3) compare with the notion of a subgroup of Z ? How does his Theorem 3.1 compare to the theorem on the subgroups of Z that we proved in class? Exercise 4. Show that Q (with addition) is not nitely generated , i.e. given any nite set r 1 ,r 2 ,...,r n Q then h r 1 ,r 2 ,...,r n i 6 = Q . [ Suggestion: Show that there are only a limited number of denominators that can be obtained from integral linear combinations of r 1 ,r 2 ,...,r n .]...
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This note was uploaded on 02/29/2012 for the course MATH 3362 taught by Professor Ryandaileda during the Spring '10 term at Trinity University.
- Spring '10