The Historical Evolution of Dirichlet's Unit Theorem
Dirichlet's unit theorem is one of the fundamental finiteness theorems in algebraic number theory.It describes the basic structure of unit groups in any algebraic number field and occupies a pivotal position in the history of algebraic number theory.Through the method of literature research and concept analysis,the origin and evolution process of the theorem are studied in this paper.The research shows that due to the research on the prime number theorem in arithmetic series,Dirichlet formulated the unit theorem and its general proof gradually.After the generalization of other mathematicians,the modern expression form of Dirichlet's unit theorem finally emerged,stating that the group of units of any algebraic number field is the direct product of its group of roots of unity and a free abelian group whose rank is finite.
Johann Peter Gustav Lejeune DirichletDirichlet's unit theoremnumber theoryideal
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