theory of modules, the radical of a module is a component in the theory of structure and classification. It is a generalization of the Jacobson radical for...

theory, the Jacobson radical of a ring R is the ideal consisting of those elements in R that annihilate all simple right R-modules. It happens that substituting...

simple right R-modules Nilradical of a ring, a nilpotent ideal which is as large as possible Radical of a module, a component in the theory of structure and...

can be considered as a dual notion to that of the radical of a module. In set notation, s o c ( M ) = ∑ N  is a simple submodule of  M N . {\displaystyle...

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...

of rings: Radical of a module Kaplansky radical Radical of a bilinear form Amitsur, S. A. (1952). "A general theory of radicals. I: Radicals in complete...

nonzero modules have maximal submodules, and also projective modules have maximal submodules. As with rings, one can define the radical of a module using...

Singular submodule Socle of a module Radical of a module Constructions Free module Quotient module Direct sum, Direct product of modules Direct limit, Inverse...

and the Radical Right," European Journal of Sociology 28: 107–151. Lua error in Module:Citation/CS1/Configuration at line 2058: attempt to index a boolean...

mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated module over a ring R may also be called a finite...

denotes the intersection of all proper maximal submodules of M (the radical of the module), then the top of M is M/rad(M). In the case of local rings with maximal...

maximal semisimple quotient of the module. Socle Radical of a module Adolfo Ballester-Bolinches, Luis M. Ezquerro, Classes of Finite Groups, 2006, ISBN 1402047185...

In abstract algebra, a uniserial module M is a module over a ring R, whose submodules are totally ordered by inclusion. This means simply that for any...

is a formal way to introduce the "denominators" to a given ring or module. That is, it introduces a new ring/module out of an existing ring/module R,...

Module theory is the branch of mathematics in which modules are studied. This is a glossary of some terms of the subject. See also: Glossary of linear...

flat modules include free modules, projective modules, and, over a principal ideal domain, torsion free modules. Formally, a module M over a ring R...

example of a bilinear form. The definition of a bilinear form can be extended to include modules over a ring, with linear maps replaced by module homomorphisms...

the Jacobson radical of a ring (typically a commutative ring) and its finitely generated modules. Informally, the lemma immediately gives a precise sense...

mathematics, a D-module is a module over a ring D of differential operators. The major interest of such D-modules is as an approach to the theory of linear...

index a boolean value. Lua error in Module:Citation/CS1/Configuration at line 2058: attempt to index a boolean value. Miller, Neil (1995). Out of the Past:...

In ring theory, a branch of mathematics, the radical of an ideal I {\displaystyle I} of a commutative ring is another ideal defined by the property that...

radical rad(R) (Lam 1999, Example 3.41). A simple module is necessarily the socle of its injective hull. The injective hull of the residue field of a...

chemistry, free-radical polymerization (FRP) is a method of polymerization by which a polymer forms by the successive addition of free-radical building blocks...

operations together give A the structure of a ring; the addition and scalar multiplication operations together give A the structure of a module or vector space...

mathematics, the Jacquet module is a module used in the study of automorphic representations. The Jacquet functor is the functor that sends a linear representation...

class group Radical of an ideal Hilbert's Nullstellensatz Flat module Flat map Flat map (ring theory) Projective module Injective module Cohen-Macaulay...

Jacobson radical. The theorem states that if R is a semiprimary ring and M is an R-module, the three module conditions Noetherian, Artinian and "has a composition...

a finite union of irreducible components. It has a straightforward extension to modules stating that every submodule of a finitely generated module over...

calls the "populist radical right" starts with the idea of 'the nation'. He however rejects the use of nationalism as a core ideology of right-wing populism...

involved in decompositions of modules, and connected to homological properties of the ring. In Boolean algebra, the main objects of study are rings in which...