Physical Sciences and Mathematics Commons^™

Finitely Generated Modules Over A Principal Ideal Domain, Mariam Mutawa Meshaab Shemal Al-Dhaheri

Theses

This thesis covers the main theory of modules: modules, submodules, cosets, quotient modules, homomorphisms, ideals, direct sums, and some related topics. Using these notions, a theorem on the structure of finitely generated modules over domains of principal ideals is proved. As an application of this theorem, the theory of the structure of normal forms of matrices over various fields is presented.