\begin{definition}[Definition:Null Sequence (Homological Algebra)]
Let $\left({R, +, \cdot}\right)$ be a ring.
Let:
:$(1): \quad \cdots \longrightarrow M_i \stackrel{d_i}{\longrightarrow} M_{i+1} \stackrel{d_{i+1}}{\longrightarrow} M_{i+2} \stackrel{d_{i+2}}{\longrightarrow} \cdots$
be a sequence of $R$-modules $M_i$ and $R$-module homomorphisms $d_i$.
Then the sequence $(1)$ is '''null''' if $d_i \circ d_{i+1} = 0$ for all $i$.
\end{definition}