Abstract
Let R be a commutative Noetherian ring and C a semidualizing module. Based on a kind of Tate \(\mathcal {F}_C\)-resolutions of modules constructed by Hu et al., in this paper, we introduce and investigate Tate homology for R-modules. For modules admitting a Tate \(\mathcal {F}_C\)-resolution, we first connect the Tate homology and corresponding relative homologies via a long exact sequence. Then we show that the vanishing of such Tate homology characterizes the finiteness of \(\mathcal {F}_C\)-projective dimension of modules. Finally, if in addition R is a Cohen–Macaulay ring with a dualizing module, we establish a balance result for such Tate homology.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
