Definition:Canonical Mapping on Free Module on Set

Definition

Let $R$ be a ring with unity.

Let $I$ be a set.

Let $R^{\paren I}$ be the free $R$-module on $I$.

The canonical mapping on $R^{\paren I}$ is the mapping $c: I \to R^{\paren I}$ defined as:

$\forall i \in I: \map c i = e_i$

where $e_i$ is the $i$th canonical basis element of $R^{\paren I}$.

Also see

• Definition:Canonical Basis of Free Module on Set