Definition:Free Module on Set
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Definition
Let $R$ be a ring.
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Let $I$ be an indexing set.
The free $R$-module on $I$ is the direct sum of $R$ as a module over itself:
- $\ds R^{\paren I} := \bigoplus_{i \mathop \in I} R$
of the family $I \to \set R$ to the singleton $\set R$.
Also see
Special case
Sources
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