Is it true that $(I\cap J)^n=I^n\cap J^n$
86816
Example of two prime ideals whose intersection of the squares not equal to the square of the intersection
13167
Prove $A = (A \setminus B) \cup (A \cap B)$
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
132541
Showing ${1\over n}\sum|S_i|=O(\sqrt n)$ for $S_i\subset [n]$, $|S_i\cap S_i|\le 1$ for $i\ne j$
33524
Prove the following $A \setminus (B\setminus C) = (A\setminus B)\cap (A \cup C)$
13421
Let $X,Y,Z$ be subspaces of $V$ so that $X$ is a subspace of $Y$. Prove that $Y\cap (X+Z)=X+(Y\cap Z)$
145058
Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $
141799
Is $2^{|\mathbb{N}|} = |\mathbb{R}|$?
14576
$(U\cap W)^0 = U^0 + W^0$
137967
Are there $a,b \in \mathbb{N}$ that ${(\sum_{k=1}^n k)}^a = \sum_{k=1}^n k^b $ beside $2,3$
65395
Prove that if $\operatorname{rank}(T) = \operatorname{rank}(T^2)$ then $R(T) \cap N(T) = \{0\}$
16749
Let $A_i= \left \{...,-2,-1,0,1,...,i \right\}$. Find $\bigcup_{i=1}^{n} A_i$ and $\bigcap_{i=1}^{n} A_i$
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
15312
Show that $R \cap R^{−1}$ is an equivalence relation on $X$?
80684
Counter example for $(A \times B) \cap (C \times D) = (A \cap C ) \times (B \cap D)$
73174
Prove $KN\cong K\times N$ if $K\cap N=\{e\}$