Definition:Linear Form

Definition
Let $R$ be a commutative ring.

Let $\left({G, +_G, \circ}\right)_R$ be a module over $R$.

Let $\phi: \left({G, +_G, \circ}\right)_R \to \left({R, +_R, \circ}\right)_R$ be a linear transformation from $G$ to the $R$-module $R$.

Then $\phi$ is called a linear form on $G$ (or linear functional).