Linear Algebra I · Dual spaces, annihilators, and transpose maps
Annihilator of an arbitrary generated supremum
Problem
For any family $(U_i)_{i\in I}$ of submodules of a $K$-module $V$, prove $(\sum_{i\in I}U_i)^{\circ}=\bigcap_{i\in I}U_i^{\circ}$.
Hint
Show an annihilator of the supremum lies in every $U_i^{\circ}$.
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