Last Updated
：2025/12/04
reduced ring
Noun
Japanese Meaning
非零の冪零元（すなわち、0でない元 x に対して、x² = 0となることがない）を持つ環。つまり、任意の元 x において、もし x² = 0 ならば x = 0 である環。
（ plural ）
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(algebra, ring theory) A ring R that has no nonzero nilpotent elements; equivalently, such that, for x ∈ R, x² = 0 implies x = 0.
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reduced ring
The spectrum of a reduced ring lacks nilpotent functions, which simplifies the study of its geometric properties.
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The spectrum of a reduced ring lacks nilpotent functions, which simplifies the study of its geometric properties.
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