-
Nilradical may
refer to:
Nilradical of a ring
Nilradical of a Lie
algebra This
disambiguation page
lists mathematics articles ****ociated with the same...
-
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...
- 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...
- M2(R). For any ring R, the
upper nilradical of Mn(R) is the set of
matrices with
entries from the
upper nilradical of R for
every positive integer n...
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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...
-
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...
- {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...
- 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...
