Let S be a multiplicative subset of a commutative ring R with identity and let T be a multiplicative subset of the ring s 1 R Let S r R r s T for some s S Then S is a multiplicative subset of R and there is a ring isomorphism s 1 R T 1 (s 1 R) ...

To prove that S is a multiplicative subset of R we need to show that it satisfies the following cond ...

Let S be a multiplicative subset of a commutative ring R with identity and let T be

Question:

Let S be a multiplicative subset of a commutative ring R with identity and let T be a multiplicative subset of the ring s^-1R. Let S_* = {r ϵ R| r/ s ϵ T for some s ϵ S}. Then S_* is a multiplicative subset of R and there is a ring isomorphism s_*^-1R ≅ T^-1(s^-1R).