Last Updated：2025/12/04
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In commutative algebra, a radical ideal is an ideal I such that whenever a power rn of an element r in the ring belongs to I for some positive integer n, then r itself belongs to I.
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In commutative algebra, a radical ideal is an ideal I such that whenever a power rn of an element r in the ring belongs to I for some positive integer n, then r itself belongs to I.
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Related words
radical ideal
Noun
Japanese Meaning
環 R のイデアル I が、自身の冪根（すなわち、任意の元 r ∈ R について、ある正の整数 n により rⁿ ∈ I ならば必ず r ∈ I となる部分集合）と一致することを意味する。 / 言い換えると、ある正の整数 n に対して rⁿ が含まれるならば、r 自身も含まれている性質を持つイデアルである。
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