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Some Results on δ-Semiperfect Rings and δ-Supplemented Modules
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  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 2,  2015, pp.289-300
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.2.289
 Title & Authors
Some Results on δ-Semiperfect Rings and δ-Supplemented Modules
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In [9], the author extends the definition of lifting and supplemented modules to -lifting and -supplemented by replacing "small submodule" with "-small submodule" introduced by Zhou in [13]. The aim of this paper is to show new properties of -lifting and -supplemented modules. Especially, we show that any finite direct sum of -hollow modules is -supplemented. On the other hand, the notion of amply -supplemented modules is studied as a generalization of amply supplemented modules and several properties of these modules are given. We also prove that a module M is Artinian if and only if M is amply -supplemented and satisfies Descending Chain Condition (DCC) on -supplemented modules and on -small submodules. Finally, we obtain the following result: a ring R is right Artinian if and only if R is a -semiperfect ring which satisfies DCC on -small right ideals of R.
-small submodules;-supplemented modules;-lifting modules;amply -supplemented modules;
 Cited by
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R. Tribak, On cofinitely lifting and cofinitely weak lifting modules, Comm. Alg., 36(12)(2008), 4448-4460. crossref(new window)

Y. Zhou, Generalizations of perfect, semiperfect and semiregular rings, Alg. Colloq., 7(3)(2000), 305-318. crossref(new window)