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Injective module

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, any…

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Injective module

Nodes120
Edges119
Triples136
Avg. degree1.98
Density0.016667
Components1

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Injective module

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related to Primary sources · 42
Injective module → Abelian, Algebra, American Mathematical Society, Archiv, Baer, BF01899665, Bulletin, Canadian Journal, Canadian Mathematical Bulletin, CJM-1963-041-4, CMB-1964-039-3, Communications, Direct, Eben, Everett, Ideals, Injective, ISSN, Joachim, Journal
related to Commutative examples · 13
Injective module → Dedekind, Eben Matlis, Every, For, In, K/R, Lam, More, R-module, R/P, RP, RP-injective, The
related to Injective cogenerators · 12
Injective module → Enochs, For, HomZ, If, It, Jenda, Maybe, Q/Z, R-module, R-modules, So, To
related to Self-injective rings · 10
Injective module → An, Artinian, Dedekind, Every, Every Frobenius, Frobenius, If, Lam, Noetherian, Th
related to Submodules, quotients, products, and sums, Bass-Papp Theorem · 10
Injective module → Any, Artinian, Bass-Papp Theorem, Every, Golan, Head, In, Lam, Noetherian, Th
related to Artinian examples · 7
Injective module → A-module, A-modules, For, Homk, If, Therefore, Translated
is a · 6
Injective module → abelian group Q/Z, direct sum of, direct sum of indecomposable injective modules and every indecomposable injective module is the injective hull of the residue field at a prime p, direct summand, module in which a homomorphism from a pure submodule can be extended to the whole module, module Q that shares certain desirable properties with the Z-module Q of all rational numbers
related to Baer's criterion · 6
Injective module → Baer's Criterion, In Baer's, More, Over, R-module, Using
related to Injective hulls · 5
Injective module → Eckmann, If, One, Schopf, The
related to Structure theorem for commutative Noetherian rings · 5
Injective module → In, Mod, Noetherian, Over, That

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injective module modules ring displaystyle every direct rings noetherian indecomposable left field r-module group category algebra hull lam 1999 one

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Injective moduleis amodule Q that shares certain desirable properties with the Z-module Q of all rational numbers0.90text
Injective moduleis adirect sum of indecomposable injective modules and every indecomposable injective module is the injective hull of the residue field at a prime p0.90text
Injective moduleis aabelian group Q/Z0.90text
Injective moduleis adirect summand0.90text
Injective moduleis adirect sum of0.90text
Injective moduleis amodule in which a homomorphism from a pure submodule can be extended to the whole module0.90text
group rings of finite groups over fieldsinstance ofRings which are themselves injective modules have a number of interesting properties and include rings0.80text
the Ext functor.The length of a finite injective resolution is the first index n such that In is nonzeroinstance ofInjective resolutions can be used to define derived functors0.80text
Iiinstance ofInjective resolutions can be used to define derived functors0.80text
Injective modulerelated to Artinian examplesIf0.60section
Injective modulerelated to Artinian examplesTranslated0.60section
Injective modulerelated to Artinian examplesHomk0.60section

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