Komplementierte Moduln über Dedekindringen
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This article is published in Journal of Algebra.The article was published on 1974-04-01 and is currently open access. It has received 70 citations till now.read more
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Modules whose maximal submodules have supplements
TL;DR: A ring R is semiperfect if and only if, for every (cyclic) R-module M, every maximal submodule has (ample) supplements in M as mentioned in this paper.
Journal ArticleDOI
On ⌖-supplemented Modules
TL;DR: In this paper, it was shown that any finite direct sum of ⌖-supplemented modules is a submodule of a right R-module, and that if every submodule has a supplement that is a direct summand of M, then it is a right-R-module.
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On some properties of ⊕-supplemented modules
A. Idelhadj,R. Tribak +1 more
TL;DR: The structure of ⊕-supplemented modules over a commutative principal ideal ring is completely determined in this article, where it is shown that every finitely generated R-module M having dual Goldie dimension less than or equal to three is a direct sum of local modules.
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On the structure of couniform and complemented modules
TL;DR: In this article, the authors investigated the structure of complemented modules over Noetherian rings and showed that every complemented module is a sum of a radical minimax module and a coatomic module.
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On -noncosingular modules
TL;DR: In this article, it was shown that for any ring R, the right R -module R is ǫ-noncosingular precisely when R has zero Jacobson radical.
References
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Injective modules over Noetherian rings.
TL;DR: In this paper, the authors studied the structure and properties of injective modules, particularly over Noetherian rings, and showed that if a module M has a maximal, injective submodule C (as is the case for left-Noetherian ring), then C contains a carbon-copy of every injective module of M, and MjC has no submodules different from 0.
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Modules with descending chain condition
TL;DR: In this paper, the Koszul complex is used to give characterizations of modules with maximal orders and decompose them uniquely into direct sums, where each summand depends on only a single maximal ideal.
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Semi-perfect modules
TL;DR: In this paper, a semi-perfect module M =.TV/R is defined over an arbi trary ring R by the following two properties: (1) the decomposition of R/J(R) can be raised to R, and (2) every cyclic right module has a projective cover.