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- Title
A note on cofinite modules over Noetherian complete local rings.
- Authors
Pirmohammadi, Gholamreza
- Abstract
Let (R, m) be a commutative Noetherian complete local ring and let I be a proper ideal of R such that the category of all I-cofinite R-modules is an Abelian subcategory of the category of all R-modules. Then for each I-cofinite R-module M it is shown that dim R/(I + AnnRM) = dim M. As a consequence of this result it is shown that if J is an ideal of R such that for each p ∈ mAssRR, dim R/(J + p) ≤ 1 or cd(J, R/p) ≤ 1, then dim R/(J + AnnRM) = dim M, for each J-cofinite R-module M.
- Subjects
NOETHERIAN rings; ABELIAN categories; LOCAL rings (Algebra); PRIME ideals
- Publication
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2022, Vol 29, Issue 4, p435
- ISSN
1370-1444
- Publication type
Article
- DOI
10.36045/j.bbms.210709