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#1 2010-04-23 21:42:21

loida
Member
Registered: 2009-11-12
Posts: 32

modules

let r be a commutative ring, I ideal in R and P r-module.
how should i prove that P/IP is module over R/I for multiplying (r+I,p+IP)-->rp+IP
and if P projective R-module, i have to prove P/IP is projective R/I-module

thanks

Last edited by loida (2010-04-23 21:47:06)

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#2 2010-04-24 04:03:39

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: modules

how should i prove that P/IP is module over R/I

The same way you prove anything is a module.  Make sure your multiplication is well-defined, and most of the other properties you don't have to check because P/IP is an R-module.

if P projective R-module, i have to prove P/IP is projective R/I-module

Any projective module is a direct summand of a free module.

"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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#3 2010-04-26 10:51:56

loida
Member
Registered: 2009-11-12
Posts: 32

tnx R

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