Abstract
Let R be a commutative Noetherian ring and I a proper ideal of R. In this paper, we study finitely generated R-modules M with only one non-vanishing local cohomology module \({H}_I^c(M)\) where \(c=cd(I,M)\). Let C be a semidualizing R-module. We investigate the conditions under which \({H}_I^c(M)\) belongs to either the Auslander class \(\mathscr{A}_C(R)\) or the Bass class \(\mathscr{B}_C(R)\).
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Ahmadi, M., Rahimi, A. Local cohomology and Foxby classes. Acta Math. Hungar. 172, 131–145 (2024). https://doi.org/10.1007/s10474-024-01391-5
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DOI: https://doi.org/10.1007/s10474-024-01391-5
Key words and phrases
- Auslander class
- Bass class
- Cohen–Macaulay module
- cohomological dimension
- derived category
- dualizing module
- Gorenstein module
- local cohomology
- semidualizing module
- system of parameters