Geodesic
On the reducing projective dimension over local rings
Glasgow mathematical journal, Tome 66 (2024) no. 1, pp. 104-118

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DOI

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.
DOI : 10.1017/S0017089523000368
Mots-clés : G-regular rings, minimal multiplicity, reducing projective and reducing Gorenstein dimension 
Celikbas, Olgur; Dey, Souvik; Kobayashi, Toshinori; Matsui, Hiroki. On the reducing projective dimension over local rings. Glasgow mathematical journal, Tome 66 (2024) no. 1, pp. 104-118. doi: 10.1017/S0017089523000368
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     title = {On the reducing projective dimension over local rings},
     journal = {Glasgow mathematical journal},
     pages = {104--118},
     year = {2024},
     volume = {66},
     number = {1},
     doi = {10.1017/S0017089523000368},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089523000368/}
}
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%D 2024
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