Complete Homology over associative rings
Olgur Celikbas, Lars Winther Christensen, Li Liang, and Greg Piepmeyer
TL;DR
This paper compares two generalizations of Tate homology, stable homology and complete homology, demonstrating their equivalence over specific classes of rings and modules.
Contribution
It establishes the equivalence of stable homology and complete homology for finitely generated modules over certain classes of rings, including Artin algebras and Gorenstein rings.
Findings
Stable homology and complete homology agree over Artin algebras.
The two theories coincide over Gorenstein and complete local noetherian rings.
Results unify different approaches to Tate homology in algebra.
Abstract
We compare two generalizations of Tate homology: stable homology and the J-completion of Tor, also known as complete homology. For finitely generated modules, we show that the two theories agree over Artin algebras and over commutative noetherian rings that are Gorenstein, or local and complete.
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