Relative stable (co)homology

Authors : Chaoling HUANG, Li YUAN

Pages : 2707-2723

View : 11 | Download : 4

Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :For a fixed precovering class $\mathcal{X}$ and a fixed preenveloping class $\mathcal{Y}$, we first introduce the notions of relative stable cohomology $\widetilde{Ext}_{\mathcal{X}}insert ignore into journalissuearticles values(-,\ -);$ and relative stable homology $\widetilde{Tor}_{\mathcal{X}\mathcal{Y}}insert ignore into journalissuearticles values(-,\ -);$. Then we consider their properties and, more importantly, we study the stable insert ignore into journalissuearticles values(co);homology under the case of $\mathcal{P}insert ignore into journalissuearticles values(R);$, $\mathcal{F}insert ignore into journalissuearticles values(R);$, and $\mathcal{I}insert ignore into journalissuearticles values(R);$ and the case of $\mathcal{P}_Cinsert ignore into journalissuearticles values(R);$, $\mathcal{F}_Cinsert ignore into journalissuearticles values(R);$, and $\mathcal{I}_Cinsert ignore into journalissuearticles values(R);$. Finally, we generalize relative stable insert ignore into journalissuearticles values(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