Abstract
We introduce the notion of Burch submodules and weakly -full submodules of modules over a local ring and study their properties. One of our main results shows that Burch submodules satisfy 2-Tor rigid and test properties. We also show that over a local ring , a submodule M of a finitely generated R-module X, such that either or ) is weakly -full in X, is 1-Tor rigid, and a test module provided that X is faithful (and has finite length when M is weakly -full). As an application, we give some new class of modules and a new class of rings such that a conjecture of Huneke and Wiegand is affirmative for them.
Citation
Souvik Dey. Toshinori Kobayashi. "Vanishing of (co)homology of Burch and related submodules." Illinois J. Math. 67 (1) 101 - 151, April 2023. https://doi.org/10.1215/00192082-10429128
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