Property: distributive

Definition: For all submodules $A,B,C$ of $M$, $A\cap(B+C)=(A\cap C)+(B\cap C)$.

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Modules

	Name
	$\bigoplus_{i=1}^\infty \mathbb Z$
	$\bigoplus_{i=1}^\infty F_2$
	$\mathbb Q$
	$\mathbb Q\times \frac{\mathbb Z}{p\mathbb Z}$, where $p$ is prime
	$\mathbb Z\times \frac{\mathbb Z}{p\mathbb Z}$, $p$ prime
	$\bigoplus_{i=1}^\infty \mathbb Z_{(2)}$
	$\mathbb R[x_1,x_2,x_3,\ldots]$
	$M_n(\mathbb Q)$
	$T_n(F_2)$
	A 2-generated faithful torsion module
	Indecomposable, not uniform module
	$(x + (x,y)^2)$
	$(x)/(x^2)$
	$2$-adic integers: $\mathbb Z_2$
	$\bigoplus_{i=0}^\infty \mathbb Q$
	$\mathbb Q^n$
	$\mathbb Z$
	$Z(p^\infty)$: the Prüfer $p$ group
	Finitely cogenerated, not Artinian
	Interval monoid ring (right regular module)
	Uniserial, not endolocal module