\begin{definition}[Definition:Linearly Dependent/Sequence]
Let $G$ be an abelian group whose identity is $e$.
Let $R$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$.
Let $\struct {G, +_G, \circ}_R$ be a unitary $R$-module.
Let $\sequence {a_k}_{1 \mathop \le k \mathop \le n}$ be a sequence of elements of $G$ such that:
:$\ds \exists \sequence {\lambda_k}_{1 \mathop \le k \mathop \le n} \subseteq R: \sum_{k \mathop = 1}^n \lambda_k \circ a_k = e$
where not all of $\lambda_k$ are equal to $0_R$.
That is, it is possible to find a linear combination of $\sequence {a_k}_{1 \mathop \le k \mathop \le n}$ which equals $e$.
Such a sequence is '''linearly dependent'''.
\end{definition}