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Studies In Free Module And It's Basis, Hsu-Chia Chen
Studies In Free Module And It's Basis, Hsu-Chia Chen
Theses Digitization Project
The purpose of this project was to study some basic properties of free modules over a ring. A module with a basis is called a free module and a free module over a division ring (or field) is called a vector space. We show every vector has a basis and any two bases of a vector space have same cardinality. However, a free module over an arbitrary ring (with identity) does not have this property.