Turkish Journal of Mathematics
DOI
10.3906/mat-1706-17
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.
Keywords
Precover, preenvelope, relative stable cohomology, relative stable homology, semidualizing module
First Page
2707
Last Page
2723
Recommended Citation
HUANG, CHAOLING and YUAN, LI
(2018)
"Relative stable (co)homology,"
Turkish Journal of Mathematics: Vol. 42:
No.
5, Article 47.
https://doi.org/10.3906/mat-1706-17
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss5/47
