Definition:Two-Sided Linear Combination in Ring
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Definition
Let $R$ be a ring.
Let $\family {x_i}_{i \mathop \in I}$ be a family of elements of $R$.
A two-sided linear combination of the family is an element of the form:
- $\ds \sum_{i \mathop \in I} a_i x_i b_i$
where:
- $\family {a_i}_{i \mathop \in I}$ and $\family {b_i}_{i \mathop \in I}$ are families in $R$ of finite support
- $\sum$ denotes summation with finite support