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Elements in a localization - category theoretic approach
This question is about the elements in a localization $S^{-1} A$ of a commutative ring $A$. Is it possible to derive $\frac{a}{1} = 0 \in S^{-1} A \Rightarrow \exists s \in S : sa = 0$ only using the ...
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Equality of elements in localization via universal property
I've been studying universal objects of universal algebra in a quite general setting and try to exhibit the structure of their elements just using the universal property. A very nice example for this ...