Category:Submodules
Jump to navigation
Jump to search
This category contains results about Submodules.
Let $\struct {R, +, \circ}$ be a ring.
Let $\struct {G, +_G}$ be an abelian group.
Let $\struct {G, +_G, \circ_G}_R$ be an $R$-module.
Let $H \subseteq G$ be a subset of $G$ which is closed for scalar product:
- $\forall \lambda \in R, x \in H: \lambda \circ x \in H$
Let $\struct {H, +_H, \circ_H}_R$ be an $R$-module where:
- $+_H$ is the restriction of $+_G$ to $H \times H$
- $\circ_H$ is the restriction of $\circ_G$ to $R \times H$.
Then $\struct {H, +_H, \circ_H}_R$ is a submodule of $\struct {G, +_G, \circ_G}_R$.
Subcategories
This category has only the following subcategory.
Pages in category "Submodules"
The following 13 pages are in this category, out of 13 total.