Date of Award

11-2015

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematical Sciences

First Advisor

Dr. Leonard D˘aus

Second Advisor

Dr. Mohamed Salim

Third Advisor

Dr. Ayman Badawi

Abstract

In this thesis we study the behavior of direct sum decomposition's in the category of modules. We present some of the most important "classical" results involving direct sum decomposition's for modules (e.g. Krull-Schmidt theorem, decomposition theorems for finitely generated modules over PID etc.). In the last part of the thesis we obtain new results, namely isomorphic refinement theorems for direct sum decomposition's of regular modules. We also obtain a link between regular modules and the exchange property.

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