| Ding分次模和强Ding分次模 |
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| 引用本文： | 韩静,梁力.Ding分次模和强Ding分次模[J].浙江大学学报(理学版),2018,45(6):656-660. |
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| 作者姓名： | 韩静 梁力 |
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| 作者单位： | 兰州交通大学 数理学院, 甘肃 兰州 730070 |
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| 基金项目： | 国家自然科学基金资助项目（11761045，11561039）；兰州交通大学“百名青年优秀人才培养计划”基金资助项目；甘肃省自然科学基金资助项目（18JR3RA113，17JR5RA091）. |
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| 摘 要： | 研究了分次环R上的Ding分次投射(内射)R-模以及强Ding分次投射(内射)R-模,证明了任意分次环上的Ding分次投射(内射)模类是投射(内射)可解的.研究了强Ding分次投射(内射)R-模与Ding分次投射(内射)R-模之间的关系,以及强Ding分次投射(内射)R-模与非分次的强Ding投射(内射)R-模之间的关系.证明了对有限群分次环R,若M是强Ding投射(内射)R-模,则F(M)是强Ding分次投射(内射)的;若N是强Ding分次投射(内射)R-模,则U(N)是强Ding投射(内射)的.
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| 关 键 词： | Ding分次投射模 Ding分次内射模 强Ding分次投射模 强Ding分次内射模 |
| 收稿时间： | 2017-12-12 |
Ding-graded modules and strongly Ding-graded modules |
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| HAN Jing,LIANG Li.Ding-graded modules and strongly Ding-graded modules[J].Journal of Zhejiang University(Sciences Edition),2018,45(6):656-660. |
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| Authors: | HAN Jing LIANG Li |
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| Affiliation: | School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China |
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| Abstract: | This paper presents a study on the Ding graded projective (injective) R-modules and strong Ding graded projective (injective) R-modules over a graded ring R. It is proved that the class of the Ding graded projective (injective) modules over any graded ring is projectively (injectively) resoluble.Some characterizations of these modules are discussed. Some relations between strongly Ding graded projective (injective) R-modules and Ding graded projective (injective) R-modules are listed. Finally, the relation between strong Ding graded projective (injective) R-modules and ungraded strong Ding projective (injective) R-modules is also studied. It is proved that for finite group graded ring R, if M is a strong Ding projective (injective) R-modules, then F(M) is a strong Ding graded projective (injective), and if N is a strong Ding graded projective (injective) R-modules, then U(N) is a strong Ding projective (injective). |
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| Keywords: | Ding gr-projective module Ding gr-injective module strongly Ding gr-projective module strongly Ding gr-injective module |
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