Associative rule of subspaces and vector spaces: $(U+V) \cap W = U + (V \cap W)$
13421
Let $X,Y,Z$ be subspaces of $V$ so that $X$ is a subspace of $Y$. Prove that $Y\cap (X+Z)=X+(Y\cap Z)$
27478
Proof that two basis of a vector space have the same cardinality in the infinite-dimensional case
121047
Proof: Sum of dimension of orthogonal complement and vector subspace
100303
A necessary and sufficient condition for $A\cap(B+C)=(A\cap B)+C$ to hold for submodules
52596
A basis for $k(X)$ regarded as a vector space over $k$
114250
If $V_0$ is the subspace of matrices of the form $C=AB-BA$ for some $A,B$ in a vector space $V$ then $V_0=\{A\in V|\operatorname{Trace} (A)=0\}$
146339
Proof of -(-v)=v in a vector space
139951
Direct Sum of vector subspaces
134909
Associativty of smash product on compact spaces
86325
Is an increasing union of subspaces a subspace?
95513
Proving $W$ is a subspace of $P_{2}$
108742
Proving commutativity of addition for vector spaces
68449
$\operatorname{Supp}(M)=V(\operatorname{Ann}M)$ if $M$ is finitely generated
95206
If $\{u,v,w\}$ is a basis for $V$, then $\{u+v+w,v+w,w\}$ is also a basis: is this proof correct?
150135
The intersection of an infinite number of subspaces is a subspace
4151
Every subspace of a vector space has a complement
124786
Prove that V contains a subspace of each dimension