Editing Characteristic polynomial (section)

==For general associative algebras==
The above definition of the characteristic polynomial of a matrix <math>A \in M_n(F)</math> with entries in a field <math>F</math> generalizes without any changes to the case when <math>F</math> is just a [[commutative ring]]. {{harvtxt|Garibaldi|2004}} defines the characteristic polynomial for elements of an arbitrary finite-dimensional ([[associative algebra|associative]], but not necessarily commutative) algebra over a field <math>F</math> and proves the standard properties of the characteristic polynomial in this generality.