- #1
jostpuur
- 2,116
- 19
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.