radical of the zero ideal. If the nilradical is the zero ideal, the ring is called a reduced ring. The nilradical of a commutative ring is the intersection...

Nilradical may refer to: Nilradical of a ring Nilradical of a Lie algebra This disambiguation page lists mathematics articles associated with the same...

In algebra, the nilradical of a Lie algebra is a nilpotent ideal, which is as large as possible. The nilradical n i l ( g ) {\displaystyle {\mathfrak...

those elements in a ring R that annihilate all simple right R-modules Nilradical of a ring, a nilpotent ideal which is as large as possible Radical of...

Jacobson radical always contains the nilradical. If the ring R is a finitely generated Z-algebra, then the nilradical is equal to the Jacobson radical, and...

{\sqrt {I}}} is the preimage of the ideal of nilpotent elements (the nilradical) of the quotient ring R / I {\displaystyle R/I} (via the natural map π...

form an ideal of R, called the nilradical of R; therefore a commutative ring is reduced if and only if its nilradical is zero. Moreover, a commutative...

{N}}} ; this is a consequence of the binomial theorem. This ideal is the nilradical of the ring. Every nilpotent element x {\displaystyle x} in a commutative...

There are, however, analogues of the nilradical defined for noncommutative rings, that coincide with the nilradical when commutativity is assumed. The concept...

ring is said to be a nil ideal if each of its elements is nilpotent. The nilradical of a commutative ring is an example of a nil ideal; in fact, it is the...