Change-of-Rings Theorems for the Small Finitistic Dimension
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913050751139840 |
|---|---|
| author | Xiong, Tao Haddaoui, Younes El Kim, Hwankoo Zhou, Qiang |
| author_facet | Xiong, Tao Haddaoui, Younes El Kim, Hwankoo Zhou, Qiang |
| contents | In this paper, we study the small finitistic dimension of a commutative ring from the viewpoint of finitistic flat homological algebra. Using the class $FPR(R)$ of modules admitting finite projective resolutions, we investigate the finitistic flat ($FT$-flat) dimension and establish several of its basic properties. We prove change-of-rings results for the $FT$-flat dimension, including quotient and polynomial extension results, as well as localization inequalities. As applications, we obtain characterizations of the small finitistic dimension in terms of $FT$-flat dimension, derive quotient and polynomial extension theorems for the small finitistic dimension, and establish local upper bounds in terms of the small finitistic dimensions of localizations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18958 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Change-of-Rings Theorems for the Small Finitistic Dimension Xiong, Tao Haddaoui, Younes El Kim, Hwankoo Zhou, Qiang Commutative Algebra Rings and Algebras Primary 13D05, Secondary 13A15, 13D07, 16S50 In this paper, we study the small finitistic dimension of a commutative ring from the viewpoint of finitistic flat homological algebra. Using the class $FPR(R)$ of modules admitting finite projective resolutions, we investigate the finitistic flat ($FT$-flat) dimension and establish several of its basic properties. We prove change-of-rings results for the $FT$-flat dimension, including quotient and polynomial extension results, as well as localization inequalities. As applications, we obtain characterizations of the small finitistic dimension in terms of $FT$-flat dimension, derive quotient and polynomial extension theorems for the small finitistic dimension, and establish local upper bounds in terms of the small finitistic dimensions of localizations. |
| title | Change-of-Rings Theorems for the Small Finitistic Dimension |
| topic | Commutative Algebra Rings and Algebras Primary 13D05, Secondary 13A15, 13D07, 16S50 |
| url | https://arxiv.org/abs/2604.18958 |