nilpotent in English

adjective
1
equal to zero when raised to a positive integral power.
He used the, now familiar, tools of idempotent and nilpotent elements.

Use "nilpotent" in a sentence

Below are sample sentences containing the word "nilpotent" from the English Dictionary. We can refer to these sentence patterns for sentences in case of finding sample sentences with the word "nilpotent", or refer to the context using the word "nilpotent" in the English Dictionary.

1. All non-zero nilpotent elements are zero divisors.

2. Unlike the quaternion algebra, the split-quaternions contain nontrivial zero divisors, nilpotent elements, and idempotents.

3. The Heisenberg group is a connected nilpotent Lie group of dimension 3, playing a key role in quantum mechanics.

4. If the symmetry algebra is either simple, or nilpotent, then the equations have families of single-valued solutions depending on two arbitrary functions of time.

5. Lie groups are classified according to their algebraic properties (simple, semisimple, solvable, nilpotent, abelian), their connectedness (connected or simply connected) and their compactness.