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

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

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

tnx R

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