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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2015.1
- 수록면
- 289 - 300 (12page)
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In [9], the author extends the definition of lifting and supplemented modules to δ-lifting and δ-supplemented by replacing "small submodule" with "δ-small submodule" introduced by Zhou in [13]. The aim of this paper is to show new properties of δ-lifting and δ-supplemented modules. Especially, we show that any finite direct sum of delta-hollow modules is delta-supplemented. On the other hand, the notion of amply δ-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 delta-supplemented and satisfies Descending Chain Condition (DCC) on δ-supplemented modules and on δ-small submodules. Finally, we obtain the following result: a ring R is right Artinian if and only if R is a δ-semiperfect ring which satisfies DCC on delta-small right ideals of R.
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참고문헌 (13)
참고문헌 신청
A. Idelhadj. / 2000 / Lecture Note of Pure and Appl. Math, 208 / Marcel Dekker : 149 ~ 155
A. Idelhadj. / 2000 / Modules for which every submodule has a supplement that is a direct summand / Arab. J. Sci. Eng. Sect. C Theme Issues 25 (2) : 179 ~ 189
A. Idelhadj. / 2003 / On some properties of ⓒ-supplemented modules / IJMMS 69 : 4373 ~ 4387
D. Keskin / 2000 / On lifting modules / Comm. Alg 28 (7) : 3427 ~ 3440
E. BAuyAuka≫s³k. / 2010 / When ±-semiperfect rings are semiperfect / Turkish J. Math 34 : 317 ~ 324
A. Idelhadj. / 2000 / Modules for which every submodule has a supplement that is a direct summand / Arab. J. Sci. Eng. Sect. C Theme Issues 25 (2) : 179 ~ 189
A. Idelhadj. / 2003 / On some properties of ⓒ-supplemented modules / IJMMS 69 : 4373 ~ 4387
D. Keskin / 2000 / On lifting modules / Comm. Alg 28 (7) : 3427 ~ 3440
E. BAuyAuka≫s³k. / 2010 / When ±-semiperfect rings are semiperfect / Turkish J. Math 34 : 317 ~ 324
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