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・ Algebraic independence
・ Algebraic integer
・ Algebraic interior
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・ Algebraic logic
・ Algebraic Logic Functional programming language
・ Algebraic manifold
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・ Algebraic modeling language
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・ Algebraic number
・ Algebraic number field
Algebraic number theory
・ Algebraic operation
・ Algebraic Petri net
・ Algebraic Reconstruction Technique
・ Algebraic Riccati equation
・ Algebraic semantics
・ Algebraic semantics (computer science)
・ Algebraic semantics (mathematical logic)
・ Algebraic sentence
・ Algebraic signal processing
・ Algebraic solution
・ Algebraic space
・ Algebraic specification
・ Algebraic statistics
・ Algebraic structure


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Algebraic number theory : ウィキペディア英語版
Algebraic number theory

Algebraic number theory is a major branch of number theory that studies algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers ''O'' in an algebraic number field ''K''/Q, and studying their algebraic properties such as factorization, the behaviour of ideals, and field extensions. In this setting, the familiar features of the integers—such as unique factorization—need not hold. The virtue of the primary machinery employed—Galois theory, group cohomology, group representations, and ''L''-functions—is that it allows one to deal with new phenomena and yet partially recover the behaviour of the usual integers.
==History of algebraic number theory==


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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