Last Updated
：2025/11/28
Eisenstein integer
Noun
Japanese Meaning
aとbが整数で、a+bωの形をとる複素数。ここでωはω³=1かつ1+ω+ω²=0を満たす複素数で、この形の数はユークリッド整域ℤ[ω]の元である。
（ plural ）
Quizzes for review
(algebra) A complex number of the form a+b𝜔, where a and b are integers and ω is defined by the following two rules: (1) 𝜔³=1 and (2) 1+𝜔+𝜔²=0; an element of the Euclidean domain ℤ[𝜔].
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Eisenstein integer
Proving that every nonzero Eisenstein integer has a unique factorization up to units and order is a fundamental result in algebraic number theory.
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Proving that every nonzero Eisenstein integer has a unique factorization up to units and order is a fundamental result in algebraic number theory.
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