Jacob Kärrlander: Classification of finitely generated modules over principal ideal domains

Abstract: As the title of this paper suggests, we will investigate the structure of finitely generated modules over principal ideal domains. This will be established by proving some important results related to this theory. In particular, we will prove structure theorems in forms of the invariant factor decomposition and the elementary divisor form. Furthermore, we will apply these results to linear algebra and study the rational canonical form of a matrix.