If $M$ is an $R$-module and $A,B,C$ are submodules of $M$ and $B$ is a submodule of $C$ then $A+ (B\cap C)=(A + B)\cap C$
100303
A necessary and sufficient condition for $A\cap(B+C)=(A\cap B)+C$ to hold for submodules
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$
103441
Proving $(A\cup B)\cap(B\cup C)\cap(C\cup A)=(A\cap B)\cup (A\cap C)\cup (B\cap C)$?
43478
Prove that: $ m_a + m_b + m_c \le 4R + r $
43990
R is a commutative ring with $1\ne 0$ and $R^m \cong R^n$, then $m=n$
37570
$M + N$ and $M \cap N$ are finitely generated $A$-modules implies $M$ and $N$ finitely generated using exact sequences
7870
For $M\otimes_R N$, why is it so imperative that $M$ be a right $R$-module and $N$ a left $R$-module?
80759
Proving $A\times (B\cap C)=(A \times B)\cap (A\times C)$.
14259
If M+N and M$\cap$N are finitely generated modules, so are M and N.
11342
Show that conguence $\bmod m\,$ is an equivalence relation
49578
Proving $a\mathbb{Z}\cap b\mathbb{Z}=[a,b]\mathbb{Z}$
66968
if $a,b$ are nilpotent elements of a commutative ring $R$, show that $a+b$ is also nilpotent
88307
Commutative property of ring addition
151803
Prove that $R$ is commutative
157309
Does $P(A\cap B) + P(A\cap B^c) = P(A)$?
92518
mod Distributive Law, factoring $\!\!\bmod\!\!:$ $\ ab\bmod ac = a(b\bmod c)$
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$