In the book A Course on Homological Algebra by Hilton-Stammbach, the authors put the following question (Chapter I, Section 5).
Develop a theorey of linear transformations $T:V\rightarrow V$ of finite dimensional vector space over $K$ by utilizing the fundamental theorem in the integral domain $K[T]$.
It is unclear to me what the "Develop a theory" stands for? In the section where this question appears, the main (fundamental) theorem of the section is that sub-modules of a free module over p.i.d. are free. Can one clarify the question a little?