In this book I treat the structure of D-module which has countable basis. If we do not care for topology of D-module, then we consider Hamel basis. If norm is defined in D-module, then we consider Schauder basis. In case of Schauder basis, we consider vectors whose expansion in the basis converges normally.
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When I began to study linear map of algebra with non commutative product, I initially was referring to finite dimensional algebra. However I saw that statements will be true for infinite dimensional algebra as well. I also I realized that some constraints for elements of algebra are required. In this book I introduce the reader to the algebra with countable basis.
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