Finite Direct Product of Unitary Modules is Unitary Module/Proof 1
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Theorem
Let $\struct {R, +_R, \times_R}$ be a ring.
Let $\struct {G_1, +_1, \circ_1}_R, \struct {G_2, +_2, \circ_2}_R, \ldots, \struct {G_n, +_n, \circ_n}_R$ be unitary $R$-modules.
Let:
- $\ds G = \prod_{k \mathop = 1}^n G_k$
be their direct product.
Then $G$ is a unitary module.
Proof
This is a special case of Direct Product of Unitary Modules is Unitary Module.