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S-injective modules

Revista De La Real Academia De Ciencias Exactas, Fisicas Y Naturales - Serie A: Matematicas, 2023
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Jongwook Baeck
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On generalized injective modules and almost injective modules

Journal of Algebra and Its Applications, 2022
A module [Formula: see text] is called [Formula: see text]-almost-invariant for a module [Formula: see text] if, for any homomorphism [Formula: see text], either [Formula: see text], or there exist nonzero direct summands [Formula: see text] of [Formula: see text] and [Formula: see text] of [Formula: see text] such that [Formula: see text] is an ...
Hayate Fuchigami   +2 more
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INJECTIVE CLASSES OF MODULES

Journal of Algebra and Its Applications, 2013
We study classes of modules over a commutative ring which allow to do homological algebra relative to such a class. We classify those classes consisting of injective modules by certain subsets of ideals. When the ring is Noetherian the subsets are precisely the generization closed subsets of the spectrum of the ring.
Chachólski, Wojciech   +2 more
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Injective modules and fp-injective modules over valuation rings

open access: yesJournal of Algebra, 2003
It is shown that each almost maximal valuation ring R such that every indecomposable injective module is countably generated, satisfies the following condition (C): each fp-injective module is locally injective. The converse holds if R is a domain. Moreover, it is proved that a valuation ring that sastisfies this condition (C) is almost maximal.
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On f -injective modules

Archiv der Mathematik, 2002
Two generalizations of injectivity are studied in this paper. An \(R\)-module \(X\) is said to be \(f\)-injective (resp. \(f^*\)-injective) if, given any monomorphism \(F\to Y\), where \(F\) is a finitely generated (resp. finitely presented) module, any homomorphism \(F\to X\) can be extended to a homomorphism \(Y\to X\).
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On injective modules and locally nilpotent endomorphisms of injective modules

Mathematical Journal of Okayama University, 1998
In the first part of this paper, the main theorem states that over a commutative Noetherian ring \(R\), an \(R\)-module \(E\) is injective if and only if every map from a prime ideal \(I\) of \(R\) into \(E\) can be extended to a map from \(R\) into \(E\).
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