In mathematics, algebraically compact modules, also called pure-injective modules, are modules that have a certain "nice" property which allows the solution...

mathematics, particularly in algebra, the class of projective modules enlarges the class of free modules (that is, modules with basis vectors) over a ring...

regarded algebraically. For a ring an ideal is primitive if and only if it is the annihilator of a simple module. It turns out that for a C*-algebra A, an...

module Finitely-generated module Finitely-presented module Finitely related module Algebraically compact module Reflexive module Concepts and theorems Composition...

W XYZ See also References algebraically compact algebraically compact module (also called pure injective module) is a module in which all systems of equations...

In algebra, given a ring R, the category of left modules over R is the category whose objects are all left modules over R and whose morphisms are all...

isomorphism. If V is an irreducible g {\displaystyle {\mathfrak {g}}} -module over an algebraically closed field and f : V → V {\displaystyle f:V\to V} is a homomorphism...

characteristic zero but is not algebraically closed, there is no general structure theory like the one for those over an algebraically closed field of characteristic...

the structure of a module or vector space over K. In this article we will also use the term K-algebra to mean an associative algebra over K. A standard...

In mathematics, the Hecke algebra of a pair (G, K) of locally compact or reductive Lie groups is an algebra of measures under convolution. It can also...

is a locally compact Hausdorff space. C*-algebras were first considered primarily for their use in quantum mechanics to model algebras of physical observables...

In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion-free modules. Formally, a module M over...

if it is algebraically compact. Ulm subgroups of cotorsion groups are cotorsion and Ulm factors of cotorsion groups are algebraically compact. Fuchs, L...

some apparently topological properties in von Neumann algebras can be defined purely algebraically. von Neumann, J. (1949), "On Rings of Operators. Reduction...

unique factorization domains ⊃ principal ideal domains ⊃ euclidean domains ⊃ fields ⊃ algebraically closed fields Formally, a rng is a set R with two binary operations...

nonassociative algebras. An algebra is a module, wherein you can also multiply two module elements. (The multiplication in the module is compatible with...

of a connected compact Lie group Highest-weight category Root system In fact, given a set of commuting matrices over an algebraically closed field, they...

space is called locally compact if, roughly speaking, each small portion of the space looks like a small portion of a compact space. More precisely, it...

\mathbb {C} } -module under scalar multipliation by complex numbers and its inner product. If X {\displaystyle X} is a locally compact Hausdorff space...

properties of the Lie algebra. It was later extended by Claude Chevalley and Samuel Eilenberg (1948) to coefficients in an arbitrary Lie module. If G {\displaystyle...

modules over a semi-simple ring must split, i.e., M ≅ M ′ ⊕ M ″ {\displaystyle M\cong M'\oplus M''} . From the point of view of homological algebra,...

of p in the affine space K n , {\displaystyle K^{n},} where K is an algebraically closed extension of k. A hypersurface may have singularities, which...

construct the moonshine module. They observed that many vertex algebras that appear 'in nature' carry an action of the Virasoro algebra, and satisfy a bounded-below...

necessarily compact), and E is a smooth vector bundle over M. Then Γ(E), the space of smooth sections of E, is a module over C∞(M) (the commutative algebra of...

In algebra, a perfect complex of modules over a commutative ring A is an object in the derived category of A-modules that is quasi-isomorphic to a bounded...

module theory, a Frobenius algebra is a finite-dimensional unital associative algebra with a special kind of bilinear form which gives the algebras particularly...

In algebra, a group ring is a free module and at the same time a ring, constructed in a natural way from any given ring and any given group. As a free...

Hopf algebra. The axioms are partly chosen so that the category of H-modules is a rigid monoidal category. The unit H-module is the separable algebra HL...

problem of classifying the simple Lie algebras. The simple Lie algebras of finite dimension over an algebraically closed field F of characteristic zero...

noncommutative algebras with additional structure. These include Drinfeld–Jimbo type quantum groups (which are quasitriangular Hopf algebras), compact matrix...