| Noether环上的Pre-内射模 |
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| 引用本文： | 向跃明. Noether环上的Pre-内射模[J]. 内蒙古师范大学学报(自然科学版), 2009, 38(4): 374-378,386 |
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| 作者姓名： | 向跃明 |
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| 作者单位： | 湖南师范大学,数学与计算机科学学院,湖南,长沙,410081;宜春学院,数学与计算机科学学院,江西,宜春,336000 |
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| 基金项目： | Project Supported by the Hunan Natural Science Foundation(08JJ3006) |
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| 摘 要： | R是环.右R-模M称为pre-内射模,如果它是一内射预盖的核.称右R-模N为强pre-内射模,如果它是一内射盖的核.得到pre-内射模的一些性质,证明了R是遗传环当且仅当任意pre-内射R-模是内射模.
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| 关 键 词： | 内射预盖 内射盖 pre-内射模 强pre-内射模 |
Pre-injective Modules on Noetherian Rings |
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| XIANG Yue-ming. Pre-injective Modules on Noetherian Rings[J]. Journal of Inner Mongolia Normal University(Natural Science Edition), 2009, 38(4): 374-378,386 |
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| Authors: | XIANG Yue-ming |
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| Affiliation: | 1.College of Mathematics and Computer Science;Hunan Normal University;Changsha 410081;China;2.College of Mathematics and Computer Science;Yichun University;Yichun 336000;Jiangxi;China |
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| Abstract: | Let R be a ring.A right R -module M is called pre-injective if it is a kernel of an injective precover;A right R -module N is called strongly pre-injective if it is a kernel of an injective cover.We show many characters of the pre-injective modules.It is shown that a ring R is right hereditary if and only if every right pre-injective R -module is injective. |
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| Keywords: | injective precover injective cover pre-injective strongly pre-injective |
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