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- Title
On the reducing projective dimension over local rings.
- Authors
Celikbas, Olgur; Dey, Souvik; Kobayashi, Toshinori; Matsui, Hiroki
- Abstract
In this paper, we are concerned with certain invariants of modules, called reducing invariants, which have been recently introduced and studied by Araya–Celikbas and Araya–Takahashi. We raise the question whether the residue field of each commutative Noetherian local ring has finite reducing projective dimension and obtain an affirmative answer for the question for a large class of local rings. Furthermore, we construct new examples of modules of infinite projective dimension that have finite reducing projective dimension and study several fundamental properties of reducing dimensions, especially properties under local homomorphisms of local rings.
- Subjects
MODULES (Algebra); FINITE rings; NOETHERIAN rings; GORENSTEIN rings; HOMOMORPHISMS; LOCAL rings (Algebra)
- Publication
Glasgow Mathematical Journal, 2024, Vol 66, Issue 1, p104
- ISSN
0017-0895
- Publication type
Article
- DOI
10.1017/S0017089523000368