Direct Sums Decompositions: Applications
Direct sums decomposition, Krull-Schmidt theorem, semi simple modules regular Modules, exchange property.In this thesis, we study the behavior of direct sum decomposition in the category Of modules. We present some of the most important "classical" result involving direct Sum decomposition for module (e.g. Krull -Schmidt theorem, decomposition theorem'For finitely generated module over PID etc.) . In the la t part of the thesis we
Obtain new result, namely isomorphic refinement theorems for direct sum decomposition Of regular modules. We also obtain a link between regular module and the Exchange property.