- nilpotent radical
- мат. нильпотентный радикал
Большой англо-русский и русско-английский словарь. 2001.
nilpotent radical
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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
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
Jacobson radical — In ring theory, a branch of abstract algebra, the Jacobson radical of a ring R is an ideal of R which contains those elements of R which in a sense are close to zero . DefinitionThe Jacobson radical is denoted by J( R ) and can be defined in the… … Wikipedia
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
Glossary of ring theory — Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. This is a glossary of some terms of the subject. Contents 1 Definition of a ring 2 Types of… … Wikipedia
Semisimple algebra — In ring theory, a semisimple algebra is an associative algebra which has trivial Jacobson radical (that is only the zero element of the algebra is in the Jacobson radical). If the algebra is finite dimensional this is equivalent to saying that it … Wikipedia
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
Core (group) — In group theory, a branch of mathematics, a core is any of certain special normal subgroups of a group. The two most common types are the normal core of a subgroup and the p core of a group. Contents 1 The normal core 1.1 Definition 1.2… … Wikipedia
Lie algebra — In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term… … Wikipedia
Corps Quadratique — Entier quadratique Pour les articles homonymes, voir Entier (homonymie). En mathématiques, un entier quadratique est un nombre réel ou complexe racine d un polynôme du second degré à coefficients dans les nombres entiers et dont le coefficient du … Wikipédia en Français
Corps quadratique — Entier quadratique Pour les articles homonymes, voir Entier (homonymie). En mathématiques, un entier quadratique est un nombre réel ou complexe racine d un polynôme du second degré à coefficients dans les nombres entiers et dont le coefficient du … Wikipédia en Français
