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Nilradical — Soit A un anneau commutatif. Définition Le nilradical de A est l ensemble des nilpotents de A. En d autres termes, c est l idéal radical de l idéal réduit à 0. Propriétés En notant Nil(A) le nilradical de A, on a les énoncés suivants : 1)… … Wikipédia en Français
Nilradical of a ring — For more radicals, see radical of a ring. In algebra, the nilradical of a commutative ring is the ideal consisting of the nilpotent elements of the ring. In the non commutative ring case, more care is needed resulting in several related radicals … Wikipedia
Nilradical of a Lie algebra — In algebra, the nilradical of a Lie algebra is a nilpotent ideal, which is as large as possible. The nilradical of a finite dimensional Lie algebra is its maximal nilpotent ideal, which exists because the sum of any two nilpotent ideals is… … Wikipedia
nilradical — noun The set of nilpotent elements of an algebraic structure such as an ideal … Wiktionary
Radical of an ideal — In ring theory, a branch of mathematics, the radical of an ideal is a kind of completion of the ideal. There are several special radicals associated with the entire ring such as the nilradical and the Jacobson radical , which isolate certain bad… … Wikipedia
Radical de un ideal — Saltar a navegación, búsqueda En teoría de anillos, una rama de las matemáticas, el radical de un anillo nos muestra ciertas propiedades malas del anillo. Hay diferentes tipos de radicales, como el nilradical o el radical de Jacobson, así como… … Wikipedia Español
Nil ideal — In mathematics, more specifically ring theory, an ideal of a ring is said to be a nil ideal if each of its elements is nilpotent.[1][2] The nilradical of a commutative ring is an example of a nil ideal; in fact, it is the ideal of the ring… … Wikipedia
Idéal premier — Richard Dedekind 1831 1916 formalisateur du concept d idéal En algèbre commutative, un idéal premier d un anneau commutatif unitaire est un idéal tel que le quotient de l anneau par cet idéal est un anneau intègre. Ce concept généralise la notion … Wikipédia en Français
Ring (mathematics) — This article is about algebraic structures. For geometric rings, see Annulus (mathematics). For the set theory concept, see Ring of sets. Polynomials, represented here by curves, form a ring under addition and multiplication. In mathematics, a… … Wikipedia
Noncommutative ring — In mathematics, more specifically modern algebra and ring theory, a noncommutative ring is a ring whose multiplication is not commutative; that is, if R is a noncommutative ring, there exists a and b in R with a·b ≠ b·a, and conversely.… … Wikipedia
