Homological dimension based on a class of Gorenstein flat modules
In this paper, we study the relative homological dimension based on the class of projectively coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and Stovicek in [26]. The resulting PGF-dimension of modules has several properties in common with the Gorenstein projective...
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Académie des sciences
2023-11-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.480/ |
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| author | Dalezios, Georgios Emmanouil, Ioannis |
| author_facet | Dalezios, Georgios Emmanouil, Ioannis |
| author_sort | Dalezios, Georgios |
| collection | DOAJ |
| description | In this paper, we study the relative homological dimension based on the class of projectively coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and Stovicek in [26]. The resulting PGF-dimension of modules has several properties in common with the Gorenstein projective dimension, the relative homological theory based on the class of Gorenstein projective modules. In particular, there is a hereditary Hovey triple in the category of modules of finite PGF-dimension, whose associated homotopy category is triangulated equivalent to the stable category of PGF-modules. Studying the finiteness of the PGF global dimension reveals a connection between classical homological invariants of left and right modules over the ring, that leads to generalizations of certain results by Jensen [24], Gedrich and Gruenberg [17] that were originally proved in the realm of commutative Noetherian rings. |
| format | Article |
| id | doaj-art-82976147a8504da6be8b6861e136304b |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-82976147a8504da6be8b6861e136304b2025-02-07T11:10:50ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-11-01361G91429144810.5802/crmath.48010.5802/crmath.480Homological dimension based on a class of Gorenstein flat modulesDalezios, Georgios0Emmanouil, Ioannis1Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, GermanyDepartment of Mathematics, University of Athens, Athens 15784, GreeceIn this paper, we study the relative homological dimension based on the class of projectively coresolved Gorenstein flat modules (PGF-modules), that were introduced by Saroch and Stovicek in [26]. The resulting PGF-dimension of modules has several properties in common with the Gorenstein projective dimension, the relative homological theory based on the class of Gorenstein projective modules. In particular, there is a hereditary Hovey triple in the category of modules of finite PGF-dimension, whose associated homotopy category is triangulated equivalent to the stable category of PGF-modules. Studying the finiteness of the PGF global dimension reveals a connection between classical homological invariants of left and right modules over the ring, that leads to generalizations of certain results by Jensen [24], Gedrich and Gruenberg [17] that were originally proved in the realm of commutative Noetherian rings.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.480/ |
| spellingShingle | Dalezios, Georgios Emmanouil, Ioannis Homological dimension based on a class of Gorenstein flat modules Comptes Rendus. Mathématique |
| title | Homological dimension based on a class of Gorenstein flat modules |
| title_full | Homological dimension based on a class of Gorenstein flat modules |
| title_fullStr | Homological dimension based on a class of Gorenstein flat modules |
| title_full_unstemmed | Homological dimension based on a class of Gorenstein flat modules |
| title_short | Homological dimension based on a class of Gorenstein flat modules |
| title_sort | homological dimension based on a class of gorenstein flat modules |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.480/ |
| work_keys_str_mv | AT daleziosgeorgios homologicaldimensionbasedonaclassofgorensteinflatmodules AT emmanouilioannis homologicaldimensionbasedonaclassofgorensteinflatmodules |