Let R be a commutative ring with identity 1R Let also D be a

Let R be a commutative ring with identity 1R. Let also D be a multiplicative subset of R

containing 1R and J be an ideal in the ring of fractions D^(1)R. Prove that the set

I = {a R | a/d J for some d D}.

is an ideal in R

Solution

Let R be a commutative ring with identity 1R. Let also D be a multiplicative subset of R containing 1R and J be an ideal in the ring of fractions D^(1)R. Prove

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