-
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 ****ociated with the same...
- 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...
-
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...
- {\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...
-
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...
- 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...
- {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...
-
split Lie
algebra E7+1/2 has a 57-dimensional
Heisenberg algebra as its
nilradical, and the
smallest possible homogeneous space for E8 is also 57-dimensional...
-
There are, however,
analogues of the
nilradical defined for
noncommutative rings, that
coincide with the
nilradical when
commutativity is ****umed. The concept...
