| Summary: | On any quiver ô��³and a field ô��, we can define a ô��-algebra which is called a
path algebra ô��ô��³. This path algebra has a basis that is the set of all paths in the quiver. Conversely, a finite dimensional algebra ô��£can be obtained by a quiver ô��³ô�®º. Furthermore, a quiver representation â�� = (ô��¸ô�¯� , ô���ô�°�) can be formed on any quiver.
A representation of a quiver �is an assignment of a vector space to each vertex and a linear mapping to each arrow. A representation which has no proper subrepresentation except zero is called a simple representation. Furthermore, if �and � are the representations of quiver �, then it can be formed a new representation which is called a direct sum of V and W and denoted by ���. A representation � of the quiver �is called indecomposable representation if � is not isomorphic to a direct sum of two nonzero representations. In this thesis, we study the properties of a representation
quiver �. Moreover, we investigate the necessary and sufficient condition of a
representation quiver � to be a simple representation and indecomposable
representation.
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