Definition:Direct Sum of Modules

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Definition

Let $A$ be a commutative ring with unity.



Let $\family {M_i}_{i \mathop \in I}$ be a family of $A$-modules indexed by $I$.



Let $M = \ds \prod_{i \mathop \in I} M_i$ be their direct product.


The direct sum $\ds \bigoplus_{i \mathop \in I} M_i$ is the submodule of $M$ the consisting of the elements of finite support.


Examples


Also see