Definition:Characteristic Polynomial of Element of Algebra

Definition
Let $A$ be a commutative ring with unity.

Let $B$ be an algebra over $A$ such that $B$ is a finite-dimensional free module over $A$.

Let $b \in B$.

The characteristic polynomial of $b$ is the characteristic polynomial of the regular representation $\lambda_b : B \to B$ over $A$.

Also see

 * Definition:Trace of Element of Algebra over Ring
 * Definition:Norm of Element of Algebra over Ring