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- Jan 29, 2012

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**Commutative ring, map R / ( I /\ J) -> ( R/I ) x ( R/J )**

I quote an unsolved question posted in MHF (November 25th, 2012) by user

**needhelp2**.

P.S.Say that R is a commutative ring and the I and J are ideals. Show that

the map : R=(I intersection J) maps to R/I R/J given by (r + (I intersection J)) maps to (r + I; r + J) is

well defined and is an injection. Show further more that is a surjection if and

only if I + J = R.

**Of course I meant in the title,**

*Communicative note**:***instead of**

*commutative***.**

*communitative*
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