$\# V(I) \le \text{dim}_K(K[X_1, \ldots, X_n]/I)$
2995
A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal
127047
How to show that $\sum_{i=1}^n | \langle f, f_i\rangle |^2 \leq \Vert f \Vert^2$
101993
The cardinality of a language over a set of variables $V$ with $\#V= κ$
92291
$U_1, U_2, ..., U_k$ subspaces of linear space $X$ with same dimensions, prove $X=U_1\oplus V=U_2\oplus V=...=U_k\oplus V$
82464
$U^*\otimes V$ versus $L(U,V)$ for infinite dimensional spaces
104258
Proof Verification: $\dim\mathrm{Im} T+\dim\ker T=\dim V$
53633
Given two subspaces $U,W$ of vector space $V$, how to show that $\dim(U)+\dim(W)=\dim(U+W)+\dim(U\cap W)$
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
52642
Show that $\text{C}/c \cong (c/(\text{C}^{\text{op}}))^{\text{op}}$
107520
Krull dimension of $\mathbb{C}[x_1, x_2, x_3, x_4]/\left$
20467
Show that $(y_n)\in l^q$
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
155066
Dimension of the quotient space $\frac{C_{0}}{M}.$
62303
For $V$ vector space of dimension $n$ under $\mathbb C$ and $T: V \to V $ linear transformation , show $V= \ker T^n \oplus $ Im $T^n$
139334
Determining the existence or non-existence of Non Trivial Ideals of $L(V)$
100161
Is it true that $\dim(X) \leq \dim(X^{\ast})$ for every infinite dimentional Banach space $X$?
41520
Prove that $L(V,W)$ forms a vector space