Turkish Journal of Mathematics
Abstract
For a fixed precovering class $\mathcal{X}$ and a fixed preenveloping class $\mathcal{Y}$, we first introduce the notions of relative stable cohomology $\widetilde{Ext}_{\mathcal{X}}(-,\ -)$ and relative stable homology $\widetilde{Tor}_{\mathcal{X}\mathcal{Y}}(-,\ -)$. Then we consider their properties and, more importantly, we study the stable (co)homology under the case of $\mathcal{P}(R)$, $\mathcal{F}(R)$, and $\mathcal{I}(R)$ and the case of $\mathcal{P}_C(R)$, $\mathcal{F}_C(R)$, and $\mathcal{I}_C(R)$. Finally, we generalize relative stable (co)homology from the case of $R$-modules to the case of $R$-complexes.
DOI
10.3906/mat-1706-17
Keywords
Precover, preenvelope, relative stable cohomology, relative stable homology, semidualizing module
First Page
2707
Last Page
2723
Recommended Citation
HUANG, C, & YUAN, L (2018). Relative stable (co)homology. Turkish Journal of Mathematics 42 (5): 2707-2723. https://doi.org/10.3906/mat-1706-17
