Definition:Submodule
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Definition
Let $\struct {R, +, \circ}$ be a ring.
Let $\struct {S, +, \circ}_R$ be an $R$-algebraic structure with one operation.
Let $T$ be a closed subset of $S$.
Let $\struct {T, +_T, \circ_T}_R$ be an $R$-module where:
- $+_T$ is the restriction of $+$ to $T \times T$
- $\circ_T$ is the restriction of $\circ$ to $R \times T$.
Then $\struct {T, +_T, \circ_T}_R$ is a submodule of $\struct {S, +, \circ}_R$.
Also see
- Results about submodules can be found here.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): $\S 27$