- 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 Nk=0{\displaystyle N^{k}=0\,} for some
positive integer k{\displaystyle k}. The smallest...
- 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...
- 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 a
commutative ring A is
locally nilpotent at a
prime ideal p if Ip, the
localization of I at p, is a
nilpotent ideal in Ap. In non-commutative algebra...
- In mathematics, a Lie
algebra g{\displaystyle {\mathfrak {g}}} is
nilpotent if its
lower central series terminates in the zero subalgebra. The
lower central...
- that H has
property P.
Common uses for this
would be when P is abelian,
nilpotent,
solvable or free. For example,
virtually solvable groups are one of the...
- a
Hilbert space is said to be
nilpotent if Tn = 0 for some n. It is said to be
quasinilpotent or
topologically nilpotent if its
spectrum σ(T) = {0}. In...
- In topology, a
branch of mathematics, a
nilpotent space,
first defined by
Emmanuel Dror (1969), is a
based topological space X such that the fundamental...
- 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...
