论文标题
相对于$ c $ - $ fp_n $ - 注射和$ c $ - $ fp_ {n} $ - 平面模块
Foxby equivalence relative to $C$-$fp_n$-injective and $C$-$fp_{n}$-flat modules
论文作者
论文摘要
令$ r $和$ s $为戒指，$ c = {} _sc_r $ a（忠实）半单字化bimodule，$ n $ a正整数或$ n = \ \ infty $。在本文中，我们介绍了$ c $ - $ fp_n $ -Indimentive $ r $ - modules和$ c $ - $ fp_n $ -flat $ s $ s $ modules，作为一些已知模块的普遍化，例如$ c $ - $ c $ - $ fp_ {n} $ - $ c $ - $ c $ - $ - $ - $ - $ - $ c $ - $ fp_ {n} $ - flat（resp。$ c $ -weak flat）$ s $ modules。然后，我们研究$ c $ - $ fp_ {n} $ - 注入和$ c $ - $ fp_ {n} $ - 模块的平面尺寸，其中这些模块的类别，即$ cfp_ni（r）_ {\ leq k} $和$ cfp_nf（r）_ {\ leq k} $和$ cfp_nf（s）我们研究了相对于这些类别的Foxby等效性，以及$ cfp_ni（r）_ {\ leq k} $和$ cfp_nf（s）_ {\ leq k} $ preendevens and Covers的存在。最后，我们研究了这些类别的交换特性，以及在几乎出色的环范围内，在几乎出色的范围下，在额外的范围内（分别为重剂）和狐狸等效性。
Let $R$ and $S$ be rings, $C= {}_SC_R$ a (faithfully) semidualizing bimodule, and $n$ a positive integer or $n=\infty$. In this paper, we introduce the concepts of $C$-$fp_n$-injective $R$-modules and $C$-$fp_n$-flat $S$-modules as a common generalization of some known modules such as $C$-$FP_{n}$-injective (resp. $C$-weak injective) $R$-modules and $C$-$FP_{n}$-flat (resp. $C$-weak flat) $S$-modules. Then we investigate $C$-$fp_{n}$-injective and $C$-$fp_{n}$-flat dimensions of modules, where the classes of these modules, namely $Cfp_nI(R)_{\leq k}$ and $Cfp_nF(S)_{\leq k}$, respectively. We study Foxby equivalence relative to these classes, and also the existence of $Cfp_nI(R)_{\leq k}$ and $Cfp_nF(S)_{\leq k}$ preenvelopes and covers. Finally, we study the exchange properties of these classes, as well as preenvelopes (resp. precovers) and Foxby equivalence, under almost excellent extensions of rings.
