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单词 Nilradical
释义

nilradical


Let R be a commutative ring. An element xR is said to be nilpotent if xn=0 for some positive integer n. The set of all nilpotent elements of R is an ideal of R, called the nilradical of R and denoted Nil(R). The nilradical is so named because it is the radicalPlanetmathPlanetmath of the zero idealMathworldPlanetmathPlanetmath.

The nilradical of R equals the prime radical of R, although proving that the two are equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath requires the axiom of choiceMathworldPlanetmath.

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更新时间:2025/5/4 2:50:52