Examples of 'nilpotent' in a sentence
Meaning of "nilpotent"
nilpotent (adjective) - In mathematics, nilpotent is used to describe an element that, when applied multiple times in a certain operation, results in zero. It is a concept commonly used in algebra and abstract algebra
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- Such that, for some positive integer n, xⁿ = 0.
- A nilpotent element.
How to use "nilpotent" in a sentence
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nilpotent
Every finitely generated nilpotent group is supersolvable.
A nilpotent matrix is a special case of a convergent matrix.
The commutator subgroup of a supersolvable group is nilpotent.
One example of a nilpotent element is a nilpotent matrix.
Nilpotent matrix and nilpotent transformation on PlanetMath.
A ring is called reduced if it has no nonzero nilpotent.
The direct product of two nilpotent groups is nilpotent.
See nilpotent matrix for more.
Hypoelliptic differential operators and nilpotent groups.
Differentials as nilpotent elements of commutative rings.
Every triangular derivation is locally nilpotent.
It is also true that finite nilpotent groups are supersolvable.
It has a normal subgroup of finite index that is nilpotent.
The trace of any power of a nilpotent matrix is zero.
The only nilpotent diagonalizable matrix is the zero matrix.
See also
There are many unstable nilpotent groups.
A nilpotent series exists if and only if the group is solvable.
We begin by describing the nilpotent operators.
Nilpotent and soluble groups.
The torsion elements in a nilpotent group form a normal subgroup.
A central series exists if and only if the group is nilpotent.
Luckily the nilpotent part of this resolution is quite accessible.
Every singular matrix can be written as a product of nilpotent matrices.
Find all nilpotent elements.
A strictly triangular matrix is nilpotent.
Nonzero nilpotent ring elements are also trivially zero divisors.
Generates a subring that is nilpotent.
Able and nilpotent groups.
A special case is whether or not every nil algebra is locally nilpotent.
The determinant and trace of a nilpotent matrix are always zero.
Clearly both of these barriers must be avoided for a nil ideal to qualify as nilpotent.
The sum of a nilpotent subring and a nil subring is always nil.
A nonzero ring in which every element is either a unit or nilpotent is a local ring.
Is also a nilpotent endomorphism.
In this phd thesis we study the central polinomials of some lie nilpotent associative algebras.
A finitely generated group is nilpotent if and only if each of its subgroups is subnormal.
Necessary conditions for local solvability of homogeneous left invariant differential operators on nilpotent lie groups.
Virtually nilpotent group.
It is straightforward to check that the group Un is nilpotent.
Infinitesimals can be made rigorous using nilpotent elements in local artin algebras.
Any nilpotent Lie algebra is a fortiori solvable but the converse is not true.
Suppose is nilpotent.
A nilpotent group G is a group with a lower central series terminating in the identity subgroup.
If f is nilpotent.
Nilpotent orbits in semisimple Lie algebras.
In the other direction the exponential map takes any nilpotent square matrix to a unipotent matrix.
Every nilpotent Lie algebra is solvable.
It is a Lie algebra analog of a nilpotent group.
The Killing form of a nilpotent Lie algebra is identically zero.
This is because any such group is a nilpotent Lie group.
