The homology of modules and modules generated by at most two elements

Güler, Sinem
Süreli Yayın başlığı
Süreli Yayın ISSN
Cilt Başlığı
Fen Bilimleri Enstitüsü
Institute of Science and Technology
The main concern of this thesis is to investigate conditions under which a module is finitely generated, and in particular under what conditions a module is generated by at most two elements. We give equivalent conditions for a module to be a direct sum of two non-isomorphic simple submodules. Using one of these conditions and the tools of homological algebra, we show that certain derived modules are trivial. The information needed for these results are collected in the fallowing chapters. That are needed in the proof of one of our new results that a Noetherian local ring possesses a non-zero finitely generated divisible module if and only if it is Artinian which is in contrast to the fact that over an integral domain R, the only finitely generated divisible module is the zero module.
Anahtar kelimeler
Algebra ,Homology ,Homological algebra, Cebir , Homoloji , Homolojik cebir