Date of Graduation
Master of Science in Mathematics
group, finitely generated abelian group, principal ideal domain, modules, ascending chain condition, basis
In this thesis, the main goal is to investigate the basic structures of finite abelian groups, finitely generated abelian groups, and finitely generated modules over principal ideal domains. We characterize finite abelian groups up to isomorphism. Then we show the existence of a set of linearly independent generators (i.e., a basis) for a finitely generated module V over a principal ideal domain. The proofs of the results leading to the basis theorem for finitely generated modules over principal ideal domains are based on a nice result in matrix theory and remain the same whether the finitely generated module V does or does not have elements of infinite order.
© Shuruq Ali Alghamdi
Alghamdi, Shuruq Ali, "Finitely Generated Abelian Groups and Bases For Finitely Generated Modules Over Principal Ideal Domains" (2014). MSU Graduate Theses. 1652.