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For every module $M$ we have a natural monomorphism $Ψ : \underset{i \in I}{∐} {H o m}_{R} (M, A_{i}) \to {H o m}_{R} (M, \underset{i \in I}{∐} A_{i})$ and we focus our attention on the case when $Ψ$ is also an epimorphism. Some other colimits are also considered.

Modules commuting (via Hom) with some limits

Robert El Bashir, Tomáš Kepka (1998)

Fundamenta Mathematicae

For every module M we have a natural monomorphism $Φ : ∐_{i \in I} H o m_{R} (A_{i}, M) \to H o m_{R} (\prod_{i \in I} A_{i}, M)$ and we focus attention on the case when Φ is also an epimorphism. The corresponding modules M depend on thickness of the cardinal number card(I). Some other limits are also considered.

Modules continus

Jacques Bichot (1971)

Publications du Département de mathématiques (Lyon)

Modules Graded by G-sets.

C. Nastasescu, F. Van Oystaeyen (1990)

Mathematische Zeitschrift

Modules injectifs indécomposables sur les anneaux artiniens et dualité de Morita

Bernard Roux (1972/1973)

Séminaire Dubreil. Algèbre et théorie des nombres

Modules of finite projective dimension and cocovers.

Dieter Happel, Luise Unger (1996)

Mathematische Annalen

Modules ordonnés injectifs

Alain Bigard (1971/1972)

Séminaire Dubreil. Algèbre et théorie des nombres

Modules Over Matrix Near-Rings and the ...-Radical.

J.D.P. Meldrum, J.H. Meyer (1991)

Monatshefte für Mathematik

Modules projectifs sur un ordre

Jacques Martinet (1970/1971)

Séminaire de théorie des nombres de Bordeaux

Modules quasi-projectifs, projectifs et parfaits

Jean-Yves Chamard (1967/1968)

Séminaire Dubreil. Algèbre et théorie des nombres

Modules sur un anneau de Krull régulier au sens de Marubayashi

J. B. Delifer (1979)

Publications du Département de mathématiques (Lyon)

Modules tertiaires

Dimitri Latsis (1976/1977)

Groupe d'étude d'algèbre Groupe d'étude d'algèbre

Modules $TTK$ -critiques et notions connexes

Jacques Raynaud (1984)

Publications du Département de mathématiques (Lyon)

Modules which are epi-equivalent to projective modules

Gary Birkenmeier (1983)

Acta Universitatis Carolinae. Mathematica et Physica

Modules which are invariant under idempotents of their envelopes

Le Van Thuyet, Phan Dan, Truong Cong Quynh (2016)

Colloquium Mathematicae

We study the class of modules which are invariant under idempotents of their envelopes. We say that a module M is -idempotent-invariant if there exists an -envelope u : M → X such that for any idempotent g ∈ End(X) there exists an endomorphism f : M → M such that uf = gu. The properties of this class of modules are discussed. We prove that M is -idempotent-invariant if and only if for every decomposition $X = ⨁_{i \in I} X_{i}$ , we have $M = ⨁_{i \in I} (u^{- 1} (X_{i}) \cap M)$ . Moreover, some generalizations of -idempotent-invariant modules are considered....

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