semisimple ideal

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• 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

• Semisimple module — In mathematics, especially in the area of abstract algebra known as module theory, a semisimple module or completely reducible module is a type of module that can be understood easily from its parts. A ring which is a semisimple module over… …   Wikipedia

• Semisimple Lie algebra — In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras, i.e., non abelian Lie algebras mathfrak g whose only ideals are {0} and mathfrak g itself. It is called reductive if it is the sum of a semisimple and an… …   Wikipedia

• Ideal (Lie-Algebra) — Lie Algebra berührt die Spezialgebiete Mathematik Lineare Algebra Lie Gruppen Physik Eichtheorie ist Spezialfall von Vektorraum …   Deutsch 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

• 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

• Von Neumann regular ring — In mathematics, a ring R is von Neumann regular if for every a in R there exists an x in R with : a = axa .One may think of x as a weak inverse of a ; note however that in general x is not uniquely determined by a .(The regular local rings of… …   Wikipedia

• List of mathematics articles (S) — NOTOC S S duality S matrix S plane S transform S unit S.O.S. Mathematics SA subgroup Saccheri quadrilateral Sacks spiral Sacred geometry Saddle node bifurcation Saddle point Saddle surface Sadleirian Professor of Pure Mathematics Safe prime Safe… …   Wikipedia

• Radical of a Lie algebra — The radical of a Lie algebra mathfrak{g} is a particular ideal of mathfrak{g}. Definition Let mathfrak{g} be a Lie algebra. The radical of mathfrak{g} is defined as the largest solvable ideal of mathfrak{g}.Such an ideal exists for the following… …   Wikipedia

• Nichols algebra — The Nichols algebra of a braided vector space (with the braiding often induced by a finite group) is a braided Hopf algebra which is denoted by and named after the mathematician Warren Nichols. It takes the role of quantum Borel part of a pointed …   Wikipedia

• Semiprimitive ring — In mathematics, especially in the area of algebra known as ring theory, a semiprimitive ring is a type of ring more general than a semisimple ring, but where simple modules still provide enough information about the ring. Important rings such as… …   Wikipedia