On the reducing projective dimension of the residue field
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866911860557611008 |
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| author | Celikbas, Olgur Dey, Souvik Kobayashi, Toshinori Matsui, Hiroki |
| author_facet | Celikbas, Olgur Dey, Souvik Kobayashi, Toshinori Matsui, Hiroki |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_09241 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the reducing projective dimension of the residue field Celikbas, Olgur Dey, Souvik Kobayashi, Toshinori Matsui, Hiroki Commutative Algebra 13D07, 13C12, 13D05, 13H10 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. |
| title | On the reducing projective dimension of the residue field |
| topic | Commutative Algebra 13D07, 13C12, 13D05, 13H10 |
| url | https://arxiv.org/abs/2207.09241 |