Last Updated
：2025/12/04
primary ideal
Noun
Japanese Meaning
準素イデアル：可換環 R のイデアル I が、任意の a,b ∈ R に対し、ab ∈ I ならば b ∈ I または a のある自然数 n (>0) に対して aⁿ ∈ I となる性質を持つこと。
（ plural ）
Quizzes for review
(algebra, ring theory) Given a commutative ring R, any ideal I such that for any a,b ∈ R, if ab ∈ I then either b ∈ I or aⁿ ∈ I for some integer n > 0.
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primary ideal
In a Noetherian ring, every primary ideal has an associated prime that controls its nilpotent elements.
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In a Noetherian ring, every primary ideal has an associated prime that controls its nilpotent elements.
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