| 弱Koszul模的若干注记 |
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| 引用本文： | 吴金勇. 弱Koszul模的若干注记[J]. 浙江大学学报(理学版), 2012, 39(4): 371-373 |
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| 作者姓名： | 吴金勇 |
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| 作者单位： | 义乌工商职业技术学院,浙江义乌,322000 |
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| 基金项目： | 浙江省教育厅资助项目(No.Y201225639) |
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| 摘 要： | 设M=i≥0Mi是弱Koszul模,则对任意的i≥0,证明了〈Mi〉[-i]是Koszul模.特别地,若M=i≥0Mi是由0次生成的分次模,则M是Koszul模当且仅当M是弱Koszul模,当且仅当对任意的i≥0,〈Mi〉[-i]是Koszul模.进一步证明了M=i≥0Mi是弱Koszul模当且仅当对任意的i≥0,有〈Ji M/Ji+1 M〉[-i]是Koszul模,其中J是Koszul代数A的分次Jacobson根.
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| 关 键 词： | Koszul代数 Koszul模 弱Koszul模 |
Notes on weakly Koszul modules |
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| WU Jin-yong. Notes on weakly Koszul modules[J]. Journal of Zhejiang University(Sciences Edition), 2012, 39(4): 371-373 |
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| Authors: | WU Jin-yong |
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| Affiliation: | WU Jin-yong (Yiwu Industrial and Commercial College,Yiwu 322000,Zhejiang Province,China) |
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| Abstract: | Some results on weakly Koszul modules are given.Let M=i≥0Mi be a weakly Koszul module.Then for all i≥0,we prove that 〈Mi〉[-i] is a Koszul module.In particular,if M=i≥0 Mi is generated in degree 0 as a graded module,then M is the Koszui if and only if M is the weakly Koszul,if and only if for all i≥0,〈Mi〉 [-i] is the Koszul.As a corollary,we have proved that M=i≥0 Mi is a weakly Koszul,if and only if for all i≥0,〈JiM/Ji+1M〉[-i] is the Koszul,where J is the graded Jacobson radical of the Koszul algebra A. |
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| Keywords: | Koszul algebras Koszul modules weakly Koszul modules |
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