Definition:Null Sequence (Homological Algebra)

Definition
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 $i$.

Also see

 * Definition:Differential Complex
 * Correspondence Between Differential Complexes and Null Sequences: due to this result, a null sequence is often also called a differential complex