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Unformatted text preview: M . Then ' ± 1 .'.A// D A C N D f a C n W a 2 A and n 2 N g : Moreover, A C N is a submodule of M containing N , and .A C N/=N Š '.A/ Š A=.A \ N/: Proof. Exercise 8.2.7 . n Exercises 8.2 R denotes a ring and M an R –module. 8.2.1. Prove Proposition 8.2.1 . 8.2.2. Prove Proposition 8.2.2 . 8.2.3. Let I be an ideal of R . Show that the quotient module M=IM has the structure of an R=I –module....
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This note was uploaded on 12/15/2011 for the course MAC 1105 taught by Professor Everage during the Fall '08 term at FSU.
- Fall '08