| 张春霞,刘仲奎.ExtF-投射生成子与ExtF-内射余生成子[J].数学年刊A辑,2018,(4):407~428 |
| ExtF-投射生成子与ExtF-内射余生成子 |
| \mathrmExtF-Projective Generators and \mathrmExtF-Injective Cogenerators |
| Received:November 22, 2016 Revised:August 24, 2017 |
| DOI：10.16205/j.cnki.cama.2018.0034 |
| 中文关键词: $mathrm{Ext}_F$-projective generator, $mathrm{Ext}_F$-injective cogenerator, $F$-resolving subcategory, $F$-coresolving subcategory, $mathcal{W}_{F}$-Gorenstein module |
| 英文关键词:$mathrm{Ext}_F$-projective generator, $mathrm{Ext}_F$-injective cogenerator, $F$-resolving subcategory, $F$-coresolving subcategory, $mathcal{W}_{F}$-Gorenstein module |
| 基金项目:本文受到国家自然科学基金(No.11261050,No.11401475)和重庆市科技计划项目(No.cstc2017jcyjAX0298)的资助. |
|
| Hits: 581 |
| Download times: 849 |
| 中文摘要: |
| 设$\mathcal{A}$ 是Abel范畴,$F$ 是$\mathrm{Ext}_{\mathcal{A}}^{1}(-,-): \mathcal{A}^{op}\times \mathcal{A}\rightarrow \mathcal{A}$
的加法子双函子. 首先研究了$\mathrm{Ext}_F${-}投射生成子与$\mathrm{Ext}_F${-}内射余生成子的同调性质,
其次引入了$\mathcal{W}_{F}${-}Gorenstein 模的概念. 特别地, 证明了如果重复$\mathcal {W}_{F}${-}Gorenstein
模的定义程序将不会产生新的模类. 最后, 统一并推广了许多参考文献中的结论. |
| 英文摘要: |
| Let $\mathcal{A}$ be an abelian category, $F$ be an additive subbifunctor of the
additive bifunctor $\mathrm{Ext}_{\mathcal{A}}^{1}(-,-): \mathcal{A}^{op}\times \mathcal{A}\rightarrow \mathcal{A}$.
This paper deals with the homological properties of $\mathrm{Ext}_F$-projective generators and $\mathrm{Ext}_F$-injective cogenerators.
As a consequence, an iteration of the procedure is used to define the $\mathcal{W}_{F}$-Gorenstein modules over
a ring $R$ yields exactly the $\mathcal{W}_{F}$-Gorenstein modules. Many results are unified and naturally generalized. |
| View Full Text View/Add Comment Download reader |
| Close |
|
|
|
|
|
