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Results tagged with noncommutative-rings
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user 345
Questions about rings that are not necessarily commutative.
4
votes
Accepted
$R/I\cong R/\text{Ann}_R(R/I)$ but $I\neq\text{Ann}_R(R/I)$
You might as well assume that $\mathrm{Ann}_R(R/I)=0$ since if $S=R/\mathrm{Ann}_R(R/I)$ then $R/I\cong S$ as $R$-modules if and only if $S/(I/\mathrm{Ann}_R(R/I))\cong S$ as $S$-modules.
So now the q …
- 3,545
2
votes
Localising a right Noetherian ring at a set of regular elements
It is not true that the right ring of fractions always exists in the setting you describe. An example where it does not can be found in section 2.1.7 of McConnell and Robson's book Noncommutative Noet …
- 3,545