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A COMPLETE DETERMINATION OF THE CUBIC CYCLIC EXTENSION FIELDS OF NUMBER FIELDS

蓝以中

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Abstract

The fundamental topic of algebraic number theory is to determine all Galois extension fields of a number field. The class field theory determines all Abelian extension fields of a number field on theoretical, but it is not concrete. The author has studied the arithmetic properties of cubic cyclic extensions of number fields in [1, 2]. In this report, we determine all cubic cyclic extension fields of any number field K.

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What this paper is about

The fundamental topic of algebraic number theory is to determine all Galois extension fields of a number field. The class field theory determines all Abelian extension fields of a number field on theoretical, but it is not concrete. The author has studied the arithmetic properties of cubic cyclic extensions of number fields in [1, 2]. In this report, we determine all cubic cyclic extension fields of any number field K.

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Available abstract

The fundamental topic of algebraic number theory is to determine all Galois extension fields of a number field. The class field theory determines all Abelian extension fields of a number field on theoretical, but it is not concrete. The author has studied the arithmetic properties of cubic cyclic extensions of number fields in [1, 2]. In this report, we determine all cubic cyclic extension fields of any number field K.

Key concepts: Extension (predicate logic), Mathematics, Genus field, Abelian extension, Algebraic number field, Class field theory, Field (mathematics), Field extension

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A COMPLETE DETERMINATION OF THE CUBIC CYCLIC EXTENSION FIELDS OF NUMBER FIELDS — Research Paper | ScholarLens