- an
element x {\displaystyle x} of a ring R {\displaystyle R} is
called nilpotent if
there exists some
positive integer n {\displaystyle n} ,
called the...
- In
linear algebra, a
nilpotent matrix is a
square matrix N such that N k = 0 {\displaystyle N^{k}=0\,} for some
positive integer k {\displaystyle k} ...
- In mathematics,
specifically group theory, a
nilpotent group G is a
group that has an
upper central series that
terminates with G. Equivalently, it has...
-
space is said to be
nilpotent if Tn = 0 for some
positive integer n. It is said to be
quasinilpotent or
topologically nilpotent if its
spectrum σ(T)...
- more
specifically ring theory, an
ideal I of a ring R is said to be a
nilpotent ideal if
there exists a
natural number k such that I k = 0. By I k, it...
- In mathematics, a Lie
algebra g {\displaystyle {\mathfrak {g}}} is
nilpotent if its
lower central series terminates in the zero subalgebra. The lower...
- In mathematics,
specifically in ring theory, a
nilpotent algebra over a
commutative ring is an
algebra over a
commutative ring, in
which for some positive...
- In topology, a
branch of mathematics, a
nilpotent space,
first defined by
Emmanuel Dror
Farjoun (1969), is a
based topological space X such that the fundamental...
- In mathematics, the
nilpotent cone N {\displaystyle {\mathcal {N}}} of a finite-dimensional
semisimple Lie
algebra g {\displaystyle {\mathfrak {g}}} is...
- trivial. For groups, the
existence of a
central series means it is a
nilpotent group; for
matrix rings (considered as Lie algebras), it
means that in...
