# Reference on Operators on Modules over PID

The operators on finite dimensional vector spaces over any field can be seen in nice form w.r.t. some choice of basis such as "diagonal, triangular, Jordan form, rational form etc." But, for operators on finitely generated modules over PID, I didn't find such theory (including minimal polynomial, characteristic polynomial, minimal polynomial divides characteristic polynomial).

Can one suggest some reference for this theory (for finitely generated modules over PID)?

(i) Concepts of minimal polynomial ($m(x)$) and characteristic polynomial ($c(x)$) for operators on finitely generated modules over PID, and whether $m(x)|c(x)$,

(ii) Jordan form of an operator

(iii) Rational form of an operator

(iv) Diagonalizable and triangulable operators.

This is equivalent to the study of modules over $R[x]$ (where $R$ is your PID) which seems difficult. For $R = k[y]$ this is the study of modules over $k[x, y]$, or the study of pairs of commuting finite-dimensional linear operators up to conjugation. – Qiaochu Yuan Jul 17 '12 at 3:08