Let V be a vector space over k and S the set of all subspaces of V. Consider the operation of subspace addition in S. Show that there is a zero in S for this operation and that the operation is associative. Consider the operation of intersection in S. Show that this operation is associative. Is there an identity for this operation (i.e., there is an E existing in S such that A intersect E = A for all E in S)?
The Attempt at a Solution
Let U and W be in S. Then U+W=W+U=0+0. U intersect W = W intersect U...I'm not really sure where else to go with this...