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nilpotent — ● nilpotent, nilpotente adjectif Élément nilpotent d un anneau A, élément a de A tel qu il existe un entier naturel non nul n pour lequel an = 0. ● nilpotent, nilpotente (expressions) adjectif Élément nilpotent d un anneau A, élément a de A tel… … Encyclopédie Universelle
nilpotent — [zu lateinisch nihil, nil »nichts«], Mathematik: 1) Ein Element a eines Ringes heißt nilpotent, wenn es eine natürliche Zahl m gibt, sodass am = 0 ist; z. B. ist im Ring der reellen 2 ☓ 2 Matrizen nilpotent wegen a2 = 0. 2) Ein (Rechts oder … Universal-Lexikon
Nilpotent — This article is about a type of element in a ring. For the type of group, see Nilpotent group. In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n such that xn = 0. The term was… … Wikipedia
Nilpotent — Ne doit pas être confondu avec Groupe nilpotent. En mathématiques, un élément x d un anneau unitaire (ou même d un pseudo anneau) R est appelé nilpotent s il existe un certain nombre entier positif n tel que . Sommaire … Wikipédia en Français
nilpotent — adjective Etymology: Latin nil nothing + potent , potens having power more at potent Date: 1870 equal to zero when raised to some power < nilpotent matrices > … New Collegiate Dictionary
Nilpotent — Das Adjektiv nilpotent (von lat. nihil = nichts, potens = fähig) tritt in der Mathematik in mehreren Bedeutungen auf: Als Eigenschaft von Matrizen, siehe nilpotente Matrix Allgemeiner als Eigenschaft von Ringelementen, siehe Nilpotenz Als… … Deutsch Wikipedia
Nilpotent orbit — Nilpotent orbits are generalizations of nilpotent matrices that play an important role in representation theory of real and complex semisimple Lie groups and semisimple Lie algebras. Contents 1 Definition 2 Examples 3 Properties … Wikipedia
Nilpotent group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product … Wikipedia
Nilpotent matrix — In linear algebra, a nilpotent matrix is a square matrix N such that for some positive integer k. The smallest such k is sometimes called the degree of N. More generally, a nilpotent transformation is a linear transformation L of a vector space… … Wikipedia
Nilpotent Lie algebra — In mathematics, a Lie algebra is nilpotent if the lower central series becomes zero eventually. Equivalently, is nilpotent if … Wikipedia
Nilpotent ideal — In mathematics, more specifically ring theory, an ideal, I, of a ring is said to be a nilpotent ideal, if there exists a natural number k such that Ik = 0.[1] By Ik, it is meant the additive subgroup generated by the set of all products of k… … Wikipedia
