| (n,m)-强投射余可解Gorenstein平坦模 |
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| 引用本文： | 钟魁晨,张翠萍,秦军霞.(n,m)-强投射余可解Gorenstein平坦模[J].山东大学学报(理学版),2023,58(2):63-71. |
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| 作者姓名： | 钟魁晨 张翠萍 秦军霞 |
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| 作者单位： | 西北师范大学数学与统计学院, 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(11761060) |
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| 摘 要： | 引入(n,m)-强投射余可解Gorenstein平坦模(即(n,m)-强PGF模)的概念,给出它的一些基本性质。证明了如果M是一个(n,m)-强PGF模,则:(1)M的PGF维数PGFd(M)≤m;(2)当1≤i≤m时,M的第i个合冲是(n,m-i)-强PGF模;当i≥m时,M的第i个合冲是(n,0)-强PGF模。其次证明了:如果模M的第d个合冲是(1,m)-强PGF模,则PGFd(M)=k≤d+m,且M是(1,k)-强PGF模。
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| 关 键 词： | PGF模 强PGF模 n-强PGF模 (n m)-强PGF模 |
(n,m)-Strongly projectively coresolved Gorenstein flat modules |
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| ZHONG Kui-chen,ZHANG Cui-ping,QIN Jun-xia.(n,m)-Strongly projectively coresolved Gorenstein flat modules[J].Journal of Shandong University,2023,58(2):63-71. |
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| Authors: | ZHONG Kui-chen ZHANG Cui-ping QIN Jun-xia |
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| Institution: | College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China |
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| Abstract: | The concept of an (n,m)-strongly projectively coresolved Gorenstein flat module(i.e.(n,m)-strongly PGF module)is introduced, and some basic properties of it are given. It is proved that if M is an (n,m)-strongly PGF module, then(1)PGF dimension of M PGFd(M)≤m;(2)when 1≤i≤m, the ith syzygy of M is(n,m-i)-strongly PGF module; when i≥m, the ith syzygy of M is(n,0)-strongly PGF module. Secondly, it is proved that the dth syzygy of M is(1,m)-strongly PGF module, then PGF d(M)=k≤d+m, and M is (1,k)-strongly PGF module. |
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| Keywords: | PGF modules strongly PGF modules n-strongly PGF modules (n m)-strongly PGF modules |
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