Matches in DBpedia 2015-10 for { <http://dbpedia.org/resource/Injective_module> ?p ?o }
- Injective_module abstract "In mathematics, especially in the area of abstract algebra known as module theory, an injective module is a module Q that shares certain desirable properties with the Z-module Q of all rational numbers. Specifically, if Q is a submodule of some other module, then it is already a direct summand of that module; also, given a submodule of a module Y, then any module homomorphism from this submodule to Q can be extended to a homomorphism from all of Y to Q. This concept is dual to that of projective modules. Injective modules were introduced in (Baer 1940) and are discussed in some detail in the textbook (Lam 1999, §3).Injective modules have been heavily studied, and a variety of additional notions are defined in terms of them: Injective cogenerators are injective modules that faithfully represent the entire category of modules. Injective resolutions measure how far from injective a module is in terms of the injective dimension and represent modules in the derived category. Injective hulls are maximal essential extensions, and turn out to be minimal injective extensions. Over a Noetherian ring, every injective module is uniquely a direct sum of indecomposable modules, and their structure is well understood. An injective module over one ring, may not be injective over another, but there are well-understood methods of changing rings which handle special cases. Rings which are themselves injective modules have a number of interesting properties and include rings such as group rings of finite groups over fields. Injective modules include divisible groups and are generalized by the notion of injective objects in category theory.".
- Injective_module thumbnail Injective_module.png?width=300.
- Injective_module wikiPageExternalLink ?id=PswhrD_wUIkC.
- Injective_module wikiPageExternalLink 1103039896.
- Injective_module wikiPageExternalLink p363.
- Injective_module wikiPageID "473775".
- Injective_module wikiPageLength "23631".
- Injective_module wikiPageOutDegree "133".
- Injective_module wikiPageRevisionID "665155954".
- Injective_module wikiPageWikiLink Abelian_group.
- Injective_module wikiPageWikiLink Abstract_algebra.
- Injective_module wikiPageWikiLink Academic_Press.
- Injective_module wikiPageWikiLink Algebraically_compact_module.
- Injective_module wikiPageWikiLink Artinian_ring.
- Injective_module wikiPageWikiLink Associative_algebra.
- Injective_module wikiPageWikiLink Basis_(linear_algebra).
- Injective_module wikiPageWikiLink Basis_of_a_vector_space.
- Injective_module wikiPageWikiLink Bimodule.
- Injective_module wikiPageWikiLink Bulletin_of_the_American_Mathematical_Society.
- Injective_module wikiPageWikiLink Canadian_Journal_of_Mathematics.
- Injective_module wikiPageWikiLink Category:Homological_algebra.
- Injective_module wikiPageWikiLink Category:Module_theory.
- Injective_module wikiPageWikiLink Category_(mathematics).
- Injective_module wikiPageWikiLink Category_of_abelian_groups.
- Injective_module wikiPageWikiLink Category_theory.
- Injective_module wikiPageWikiLink Characteristic_(algebra).
- Injective_module wikiPageWikiLink Circle_group.
- Injective_module wikiPageWikiLink Commutative_diagram.
- Injective_module wikiPageWikiLink Commutative_ring.
- Injective_module wikiPageWikiLink Completion_(algebra).
- Injective_module wikiPageWikiLink Completion_(ring_theory).
- Injective_module wikiPageWikiLink Contravariant_functor.
- Injective_module wikiPageWikiLink Cyclic_module.
- Injective_module wikiPageWikiLink Dedekind_domain.
- Injective_module wikiPageWikiLink Derived_category.
- Injective_module wikiPageWikiLink Derived_functor.
- Injective_module wikiPageWikiLink Dimension_(vector_space).
- Injective_module wikiPageWikiLink Dimension_of_a_vector_space.
- Injective_module wikiPageWikiLink Direct_sum.
- Injective_module wikiPageWikiLink Direct_sum_of_modules.
- Injective_module wikiPageWikiLink Direct_summand.
- Injective_module wikiPageWikiLink Divisible_group.
- Injective_module wikiPageWikiLink Divisible_module.
- Injective_module wikiPageWikiLink Duality_of_categories.
- Injective_module wikiPageWikiLink Eben_Matlis.
- Injective_module wikiPageWikiLink Endomorphism_ring.
- Injective_module wikiPageWikiLink Equivalence_of_categories.
- Injective_module wikiPageWikiLink Essential_extension.
- Injective_module wikiPageWikiLink Exact_functor.
- Injective_module wikiPageWikiLink Exact_sequence.
- Injective_module wikiPageWikiLink Ext_functor.
- Injective_module wikiPageWikiLink Factor_group.
- Injective_module wikiPageWikiLink Field_(mathematics).
- Injective_module wikiPageWikiLink Field_of_fractions.
- Injective_module wikiPageWikiLink Finite_group.
- Injective_module wikiPageWikiLink Finitely-generated_module.
- Injective_module wikiPageWikiLink Finitely_generated_module.
- Injective_module wikiPageWikiLink Flat_module.
- Injective_module wikiPageWikiLink Formal_power_series.
- Injective_module wikiPageWikiLink Free_module.
- Injective_module wikiPageWikiLink Frobenius_algebra.
- Injective_module wikiPageWikiLink Functor.
- Injective_module wikiPageWikiLink Functor_category.
- Injective_module wikiPageWikiLink Group_algebra.
- Injective_module wikiPageWikiLink Group_representation.
- Injective_module wikiPageWikiLink Group_ring.
- Injective_module wikiPageWikiLink Hereditary_ring.
- Injective_module wikiPageWikiLink Ideal_(ring_theory).
- Injective_module wikiPageWikiLink Indecomposable_module.
- Injective_module wikiPageWikiLink Injective.
- Injective_module wikiPageWikiLink Injective_cogenerator.
- Injective_module wikiPageWikiLink Injective_function.
- Injective_module wikiPageWikiLink Injective_hull.
- Injective_module wikiPageWikiLink Injective_module.
- Injective_module wikiPageWikiLink Injective_object.
- Injective_module wikiPageWikiLink Integral_domain.
- Injective_module wikiPageWikiLink Journal_of_Algebra.
- Injective_module wikiPageWikiLink Linear_span.
- Injective_module wikiPageWikiLink Local_ring.
- Injective_module wikiPageWikiLink Localization_of_a_ring.
- Injective_module wikiPageWikiLink Mathematics.
- Injective_module wikiPageWikiLink Module_(mathematics).
- Injective_module wikiPageWikiLink Module_homomorphism.
- Injective_module wikiPageWikiLink Module_theory.
- Injective_module wikiPageWikiLink Monomorphism.
- Injective_module wikiPageWikiLink Noetherian_ring.
- Injective_module wikiPageWikiLink Pacific_Journal_of_Mathematics.
- Injective_module wikiPageWikiLink Polynomial_ring.
- Injective_module wikiPageWikiLink Prime_ideal.
- Injective_module wikiPageWikiLink Prime_spectrum.
- Injective_module wikiPageWikiLink Principal_ideal_domain.
- Injective_module wikiPageWikiLink Product_(category_theory).
- Injective_module wikiPageWikiLink Projective_module.
- Injective_module wikiPageWikiLink Prüfer_group.
- Injective_module wikiPageWikiLink Publicationes_Mathematicae_Debrecen.
- Injective_module wikiPageWikiLink Pure_injective_module.
- Injective_module wikiPageWikiLink Pure_submodule.
- Injective_module wikiPageWikiLink Quasi-Frobenius_ring.
- Injective_module wikiPageWikiLink Quotient_group.
- Injective_module wikiPageWikiLink Quotient_module.