Nilpotent

Quick meaning: Nilpotent is an adjective meaning (mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.

Meaning

(mathematics, algebra, ring theory, of an element x of a ring) Such that, for some positive integer n, xⁿ = 0.

More Meanings

1. (algebra) A nilpotent element.
2. (mathematics, algebra) 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.

Example Sentences

If a square matrix is upper triangular and has zeros on the diagonal, then it is nilpotent (under the usual matrix multiplication).

The so-called spinor algebra of C(2), the language of the quantum mechanics, is formulated in terms of the idempotents and nilpotents of the geometric algebra of space, including its beautiful representation on the Riemann sphere, and a new proof of the Heisenberg uncertainty principle.

The rest of this book is devoted to determining the conjugacy classes and centralizers of nilpotent elements in L(G) and unipotent elements in G, where G is an exceptional algebraic group of type E₈,E₇, E₆, F₄ or G₂ over an algebraically closed field K of characteristic p. This chapter contains statements of the main results for nilpotent elements.

Word Forms

• nilpotents

Related Words

Related dictionary entries include nullary, idempotent, effective, quasinilpotent, nonzero, unipotent.

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