Basic Morita Equivalent Over Arbitrary Fields

For tracking the local structure between the block algebras under Morita equivalent, Puig defines the basic Morita equivalent When k is an algebraically closed field, Puig obtains the structure relationship between the source algebras of block algebras which are basic Morita equivalent. In this thesis, we define the basic Morita equivalent under the situation of arbitrary fields, and obtain the local structure relationship between the source algebras of block algebras.