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Jun 25, 2013 at 3:02 review Late answers
Jun 25, 2013 at 14:05
Mar 8, 2010 at 21:11 comment added user3795 Fair enough. They are in the case where $A$ is a commutative ring with unit and $1\in A$. Should have written those pre-suppositions into my write-up above (which I have improved upon personally but not yet edited). It also is unclear in your original question exactly what isomorphism (or equality) you want to show via the universal property.
Mar 8, 2010 at 13:42 comment added Martin Brandenburg No. $A$ and $S^{-1} A$ are not isomorphic.
Feb 15, 2010 at 15:57 history answered user3795 CC BY-SA 2.5