Results 31 to 40 of about 607,054 (303)
Copure direct injective modules
, 2021 In this paper, we have introduced copure-direct-injective modules. A right R-module M is said to be copure-direct-injective if every copure submodule of M isomorphic to a direct summand of M is itself a direct
Toksoy, Sultan Eylem +1 more
core +1 more source
Results in Injective Envelope and Indecomposable Injective Modules
پژوهشهای ریاضی, 2021 Introduction Throughout this paper, is a commutative ring with non-zero identity and is an -module. The study of injective modules is very important in commutative algebra and homological Algebra.
Masoumeh Hasanzad +2 more
doaj
Journal of Mathematics, 2022 In this paper, we investigate the notions of X⊥-projective, X-injective, and X-flat modules and give some characterizations of these modules, where X is a class of left modules. We prove that the class of all X⊥-projective modules is Kaplansky.
Arunachalam Umamaheswaran +4 more
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Glasgow Mathematical Journal, 2010 AbstractSince Azumaya introduced the notion of A-injectivity in 1974, several generalizations have been investigated by a number of authors. We introduce some more generalizations and discuss their connection to the previous ones.
KESKİN TÜTÜNCÜ, DERYA +2 more
openaire +3 more sources
On the Number of Injective Indecomposable Modules [PDF]
Journal of Algebra, 2001 Let \(R\) be a valuation ring, i.e., \(R\) is a subring of a skew field \(F\) such that \(a\in F\setminus R\) implies \(a^{-1}\in R\). Let \(E\) be an indecomposable injective right \(R\)-module and denote \(P(E)=\{p\in R\mid\exists 0\neq m\in E\text{ with }mp=0\}\).
Brungs, Hans-Heinrich, Törner, Günter
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ON THE PROJECTIVE DIMENSION OF ARTINIAN MODULES [PDF]
Journal of Algebraic Systems, 2021 Let $(R, \mathfrak{m})$ be a Noetherian local ring and $M$, $N$ be two finitely generated $R$-modules. In this paper it is shown that $R$ is a Cohen-Macaulay ring if and only if $R$ admits a non-zero Artinian $R$-module $A$ of finite projective dimension;
Y. Irani, K. Bahmanpour, Gh. Ghasemi
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Idempotent Reflexive rings whose every simle singular right module are yj-injective [PDF]
المجلة العراقية للعلوم الاحصائية, 2011 In this paper we study rightidempotent reflexive ring whose simple singular right R-module isYJ-injective, we prove that this type of ring is right weakly regular ring, we show that if R is N duo or NCI ring and R is right idempotent reflexive ring ...
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A note on a generalization of injective modules
Karpatsʹkì Matematičnì Publìkacìï, 2020 As a proper generalization of injective modules in term of supplements, we say that a module $M$ has the property (ME) if, whenever $M\subseteq N$, $M$ has a supplement $K$ in $N$, where $K$ has a mutual supplement in $N$. In this study, we obtain that $(
B.N. Türkmen, E. Türkmen
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Journal of Mathematics, 2022 The LA-module is a nonassociative structure that extends modules over a nonassociative ring known as left almost rings (LA-rings). Because of peculiar characteristics of LA-ring and its inception into noncommutative and nonassociative theory, drew the ...
Asima Razzaque, Inayatur Rehman
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Gillespie’s questions and Grothendieck duality
Comptes Rendus. Mathématique, 2021 Gillespie posed two questions in [Front. Math. China 12 (2017) 97-115], one of which states that “for what rings $R$ do we have $\mathrm{K}(\mathrm{AC})=\mathrm{K}(R\text{-}\mathrm{Inj})$?”. We give an answer to such a question.
Wang, Junpeng, Liu, Zhongkui, Yang, Gang
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