Let $R$, $S$, and $T$ be subspaces of a vector space.
I was able to show that $(R \cap T)+(S \cap T) \subseteq (R+S) \cap T$.
So my question now is: When will equality happen without using the other inclusion?
Let $R$, $S$, and $T$ be subspaces of a vector space.
I was able to show that $(R \cap T)+(S \cap T) \subseteq (R+S) \cap T$.
So my question now is: When will equality happen without using the other inclusion?