Prove that If $dim_F$ $(V ) > 1$ be finite, prove that $L(V )$ has two sided ideals other than $(0)$ and $L(V )$.
Further
Prove that the conclusion above is false if $V$ is not finite dimensional over $F$.
If $dim_F$ $(V ) > 1$.Then let $v_1,v_2$ be two basis elements of $V$.The I tried making an ideal of $L(V )$ using these two basis elements but I was unsucessful.
Please help me with the problem.I tried the last part too but wasn't sucessful
Note that the above is false as written. See the dupliacte for the correct assertion.
