Definition of Nilpotent. Meaning of Nilpotent. Synonyms of Nilpotent

Here you will find one or more explanations in English for the word Nilpotent. Also in the bottom left of the page several parts of wikipedia pages related to the word Nilpotent and, of course, Nilpotent synonyms and on the right images related to the word Nilpotent.

Definition of Nilpotent

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Meaning of Nilpotent from wikipedia

- 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 mathematics, specifically group theory, a nilpotent group G is a group that has an upper central series that terminates with G. Equivalently, it has...
- 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} ...
- 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, the nilpotent cone N {\displaystyle {\mathcal {N}}} of a finite-dimensional semisimple Lie algebra g {\displaystyle {\mathfrak {g}}} is...
- 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 mathematics, nilpotent orbits are generalizations of nilpotent matrices that play an important role in representation theory of real and complex semisimple...
- 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...