- #1
steenis
- 312
- 18
Let ##M## be a (right) R-module, and ##A## and ##B## two submodules of ##M##.
If ##A = B ##, then we know that ##\frac{M}{A} = \frac{M}{B}##.
But is the converse also true:
If ##\frac{M}{A} = \frac{M}{B}##, can we conclude that ##A = B ## ?
I doubt it, but I cannot find the answer. Maybe someone can help me with a proof or a counterexample ?
(If possible, also a reference.)
If ##A = B ##, then we know that ##\frac{M}{A} = \frac{M}{B}##.
But is the converse also true:
If ##\frac{M}{A} = \frac{M}{B}##, can we conclude that ##A = B ## ?
I doubt it, but I cannot find the answer. Maybe someone can help me with a proof or a counterexample ?
(If possible, also a reference.)