Definition:Ring of Linear Operators
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Definition
Let $R$ be a ring.
Let $G$ be an $R$-module.
Let $\map {\LL_R} G$ denote the set of all linear operators on $G$.
Let $+$ and $\circ$ be the binary operations on $\map {\LL_R} G$ defined such that:
- $+$ denotes pointwise addition
- $\circ$ denotes composition of linear operators.
Then the algebraic structure:
- $\struct {\map {\LL_R} G, +, \circ}$ is a ring
is known as the ring of linear operators on $G$.