In algebra, the nilradical of a commutative ring is the ideal consisting of the nilpotent elements: N R = N i l ( R ) = { f ∈ R ∣ f m = 0 for some m ∈ Z > 0 } . {\displaystyle {\mathfrak {N}}_{R}=\mathrm {Nil} (R)=\lbrace f\in R\mid f^{m}=0{\text{ for some }}m\in \mathbb {Z} _{>0}\rbrace .} It is thus the radical of the zero ideal and is also denoted ( 0 ) {\displaystyle {\sqrt {(0)}}} or r a d ( 0 ) {\displaystyle \mathrm {rad} (0)} .
In algebra, the nilradical of a commutative ring is the ideal consisting of the nilpotent elements: N R = N i l ( R ) = { f ∈ R ∣ f m = 0 for some m ∈ Z > 0 } . {\displaystyle {\mathfrak {N}}_{R}=\mathrm {Nil} (R)=\lbrace f\in R\mid f^{m}=0{\text{ for some }}m\in \mathbb {Z} _{>0}\rbrace .} It is thus the radical of the zero ideal and is also denoted ( 0 ) {\displaystyle {\sqrt {(0)}}} or r a d ( 0 ) {\displaystyle \mathrm {rad} (0)} .
Source: Wikipedia "Nilradical of a ring" · CC BY-SA 4.0
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