Suppose [itex]A\subset\mathfrak{g}[/itex] and [itex]I\subset\mathfrak{g}[/itex] are subalgebras of some Lie algebra, and I is an ideal. Is there something wrong with an isomorphism [itex](A+I)/I \simeq A/I[/itex], [itex]a+i+I=a+I\mapsto a+I[/itex], for [itex]a\in A[/itex] and [itex]i\in I[/itex]? I cannot see what could be wrong, but all texts always give a theorem [itex](I+J)/J\simeq I/(I\cap J)[/itex] instead.(adsbygoogle = window.adsbygoogle || []).push({});

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# Lie algebra, ideal and isomorphism

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