外来
发表于 2025-3-26 22:03:48
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Extort
发表于 2025-3-27 04:13:01
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污点
发表于 2025-3-27 08:26:22
Commutative FieldsFor the convenience of the reader we recall some definitions and facts about commutative fields.
Anguish
发表于 2025-3-27 09:33:23
Residue ClassesIn this chapter, we study residue classes modulo a natural number. This leads to the consideration of groups. Therefore it is convenient to recall that if . is a finite group, the number of elements of . is called the . of ., denoted by ..
配置
发表于 2025-3-27 16:22:00
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goodwill
发表于 2025-3-27 20:56:48
Algebraic IntegersThe arithmetic of the field of rational numbers is mainly the study of divisibility properties with respect to the ring of integers.
贸易
发表于 2025-3-28 00:01:10
Integral Basis, DiscriminantWe have seen in the numerical examples of the preceding chapter that the ring of algebraic integers of a quadratic number field, and also of the cyclotomic field ℚ(ζ) (where ζ is a primitive .th root of unity), are free finitely generated Abelian groups.
Obstruction
发表于 2025-3-28 05:55:02
The Decomposition of IdealsWe have shown that the ring . of algebraic integers of an algebraic number field is Noetherian and integrally closed. However, it is not true in general that . is a principal ideal domain.
ADJ
发表于 2025-3-28 10:18:28
The Norm and Classes of IdealsWe know already that the ring . of integers of an algebraic number field . need not be a principal ideal domain. In this chapter, we associate with every field . a numerical invariant ., which measures the extent to which . deviates from being a principal ideal domain. . will be equal to 1 if and only if . is a principal ideal domain.
OGLE
发表于 2025-3-28 14:12:11
Estimates for the DiscriminantIn this chapter we study the discriminant. A method of “Geometry of Numbers” is used to provide sharper estimates for the discriminant.