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Communications in Algebra, 2009 In this article, we define a module M to be 𝒢-extending if and only if for each X ≤ M there exists a direct summand D of M such that X ∩ D is essential in both X and D. We consider the decomposition theory for 𝒢-extending modules and give a characterization of the Abelian groups which are 𝒢-extending.
Evrim Akalan +2 more
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On generalized extending modules
Journal of Zhejiang University: Science A, 2007A module \(M\) is called generalized extending if every submodule \(N\) of \(M\) is contained in a direct summand \(K\) of \(M\) such that \(K/N\) is a singular module. Basic properties of such modules are studied, including a characterization of those rings \(R\) such that every \(R\)-module is generalized extending.
Qingyi Zeng
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Algebras and Representation Theory, 2009
The author describes in a common language two generalizations of extending modules studied by \textit{P. F. Smith, D. V. Huynh} and \textit{N. V. Dung} [in Q. J. Math., Oxf. II. Ser. 41, No. 162, 225-235 (1990; Zbl 0712.16016)] and by \textit{J. Clark} [in Abelian groups and modules. Proc. int. conf. Dublin, 1998. Basel: Birkhäuser.
Septimiu Crivei
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The author describes in a common language two generalizations of extending modules studied by \textit{P. F. Smith, D. V. Huynh} and \textit{N. V. Dung} [in Q. J. Math., Oxf. II. Ser. 41, No. 162, 225-235 (1990; Zbl 0712.16016)] and by \textit{J. Clark} [in Abelian groups and modules. Proc. int. conf. Dublin, 1998. Basel: Birkhäuser.
Septimiu Crivei
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Modules which are Weak Extending Relative to Module Classes [PDF]
Acta Mathematica Hungarica, 2000 Two notions of weak extending modules with respect to a class of modules \(\mathcal X\) are introduced and related to other notions of extending relative to a module class. An \(R\)-module \(M\) is called weak type \(1\) \(\mathcal X\)-extending if for every \(\mathcal X\)-submodule \(N\) of \(M\) there exists a complement \(K\) of \(N\) in \(M\) such ...
Dogruöz, S, Smith, PF
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Extending Endo-monomial Modules
Algebra Colloquium, 2013 Let G be a finite group with a normal Sylow p-subgroup P. Let [Formula: see text] be a complete discrete valuation ring with residue field F of characteristic p. Let M be an indecomposable endo-monomial [Formula: see text]-module. In this paper we prove that M extends to an [Formula: see text]-module if and only if M is G-stable.
Lu, Ziqun, Zhang, Jiping
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PURELY e*-EXTENDING MODULES AND e*-SUPPLEMENT EXTENDING MODULES
Missouri Journal of Mathematical SciencesHiba R. Baanoon, Abdulkareem Ali
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ON MODULES AND MATRIX RINGS WITH SIP-EXTENDING [PDF]
Taiwanese Journal of Mathematics, 2007 In this note we study modules with the property that the intersection of two direct summands is essential in a direct summand (SIP-extending). Amongst other results we show that the class of right SIP-extending modules is neither closed under direct sums
Tercan, A. +3 more
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