English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

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 theconcepts of $C$-$fp_n$-injective $R$-modules and $C$-$fp_n$-flat $S$-modules asa common generalization of some known modules such as $C$-$FP_{n}$-injective(resp. $C$-weak injective) $R$-modules and $C$-$FP_{n}$-flat (resp. $C$-weakflat) $S$-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 studyFoxby 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 ofrings.

Foxby equivalence relative to $C$-$fp_n$-injective and $C$-$fp_{n}$-flat modules