| 关于$(m,n)$-凝聚模与预包络 |
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| 引用本文： | 宋贤梅,陈建龙.关于$(m,n)$-凝聚模与预包络[J].数学研究与评论,2008,28(1):57-66. |
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| 作者姓名： | 宋贤梅 陈建龙 |
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| 作者单位： | [1]Department of Mathematics, Anhui Normal University, Anhui 241000, China; [2]Department of Mathematics, Southeast University, Jiangsu 210096, China |
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| 基金项目： | the National Natural Science Foundation of China （No. 10571026）; the Natural Science Foundation of Anhui Provincial Education Department （No. 2006kj050c）; Doctoral Foundation of Anhui Normal University. |
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| 摘 要： | In this paper, let m, n be two fixed positive integers and M be a right R-module, we define （m, n）-M-flat modules and （m, n）-coherent modules. A right R-module F is called （m, n）-M-flat if every homomorphism from an （n, m）-presented right R-module into F factors through a module in addM. A left S-module M is called an （m, n）-coherent module if MR is finitely presented, and for any （n, m）-presented right R-module K, Hom（K, M） is a finitely generated left S-module, where S = End（MR）. We mainly characterize （m, n）-coherent modules in terms of preenvelopes （which are monomorphism or epimorphism） of modules. Some properties of （m, n）-coherent rings and coherent rings are obtained as corollaries.
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| 关 键 词： | （m n）-凝聚模 预包络 （m n）-M-平坦模 （m n）-M-平坦预均衡 |
| 收稿时间： | 2006-01-03 |
| 修稿时间： | 2006-08-26 |
On $(m,n)$-Coherent Modules and Preenvelopes |
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| SONG Xian-mei and CHEN Jian-long.On $(m,n)$-Coherent Modules and Preenvelopes[J].Journal of Mathematical Research and Exposition,2008,28(1):57-66. |
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| Authors: | SONG Xian-mei and CHEN Jian-long |
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| Institution: | Department of Mathematics, Anhui Normal University, Anhui 241000, China;Department of Mathematics, Southeast University, Jiangsu 210096, China |
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| Abstract: | In this paper, let $m,n$ be two fixed positive integers and $M$ be a right $R$-module, we define $(m,n)$-$M$-flat modules and $(m,n)$-coherent modules. A right $R$-module $F$ is called $(m,n)$-$M$-flat if every homomorphism from an $(n,m)$-presented right $R$-module into $F$ factors through a module in ${\rm add}M$. A left $S$-module $M$ is called an $(m,n)$-coherent module if $M_{R}$ is finitely presented, and for any $(n,m)$-presented right $R$-module $K$, ${\rm Hom}(K,M)$ is a finitely generated left $S$-module, where $S={\rm End}(M_{R})$. We mainly characterize $(m,n)$-coherent modules in terms of preenvelopes (which are monomorphism or epimorphism) of modules. Some properties of $(m,n)$-coherent rings and coherent rings are obtained as corollaries. |
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| Keywords: | $(m n)$-$M$-flat module $(m n)$-coherent module $(m n)$-$M$-flat preenvelope |
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