On this page you'll find 9 example sentences with Nilpotent. Discover the meaning, synonyms such as digit or figure and how to use the word correctly in a sentence.
Nilpotent meaning
- Such that, for some positive integer n, xⁿ = 0.
- In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior.
- Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
Using Nilpotent
- The main meaning on this page is: Such that, for some positive integer n, xⁿ = 0. | In any of several technical senses: behaving analogously to nilpotent ring elements as an element of some other algebraic structure; composed of elements displaying such behavior. | Belonging to the derived algebra of L and such that the adjoint action of x is nilpotent (as a linear transformation on L).
- Useful related words include: digit, figure.
- In the example corpus, nilpotent often appears in combinations such as: nilpotent elements, nilpotent element, nilpotent and.
Context around Nilpotent
- Average sentence length in these examples: 18.6 words
- Position in the sentence: 3 start, 4 middle, 2 end
- Sentence types: 9 statements, 0 questions, 0 exclamations
Corpus analysis for Nilpotent
- In this selection, "nilpotent" usually appears in the middle of the sentence. The average example has 18.6 words, and this corpus slice is mostly made up of statements.
- Around the word, define, via, elements, element and matrix stand out and add context to how "nilpotent" is used.
- Recognizable usage signals include a nilpotent element in and algebra is nilpotent if the. That gives this page its own corpus information beyond isolated example sentences.
- By corpus frequency, "nilpotent" sits close to words such as aakash, aanholt and aardwolf, which helps place it inside the broader word index.
Example types with nilpotent
The same corpus examples are grouped by length and sentence type, making it easier to see the contexts in which the word appears:
Commutators are used to define nilpotent and solvable groups. (9 words)
The trace of any power of a nilpotent matrix is zero. (11 words)
A nilpotent element in a nonzero ring is necessarily a zero divisor. (12 words)
In fact for any ring, the nilpotent elements in the center of the ring are also in the Jacobson radical.sfn So, for commutative rings, the nilradical is contained in the Jacobson radical. (33 words)
This can be used to reduce some problems about Lie groups (such as finding their unitary representations) to the same problems for connected simple groups and nilpotent and solvable subgroups of smaller dimension. (33 words)
The construction via nilpotent elements is more fundamental in the sense that an idempotent may then be produced from it. (20 words)
Example sentences (9)
A Lie algebra is nilpotent if the lower central series : becomes zero eventually.
A nilpotent element in a nonzero ring is necessarily a zero divisor.
Commutators are used to define nilpotent and solvable groups.
Hence, ũ can directly be identified with the nilpotent element of the basis of the dual numbers.
If N is the nilradical of commutative ring R, then the quotient ring R/N has no nilpotent elements.
In fact for any ring, the nilpotent elements in the center of the ring are also in the Jacobson radical.sfn So, for commutative rings, the nilradical is contained in the Jacobson radical.
The construction via nilpotent elements is more fundamental in the sense that an idempotent may then be produced from it.
The trace of any power of a nilpotent matrix is zero.
This can be used to reduce some problems about Lie groups (such as finding their unitary representations) to the same problems for connected simple groups and nilpotent and solvable subgroups of smaller dimension.
Common combinations with nilpotent
These word pairs occur most frequently in English texts: