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Homological dimension based on a class of Gorenstein flat modules
Dalezios, Georgios1 ; Emmanouil, Ioannis2 
1 Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
2 Department of Mathematics, University of Athens, Athens 15784, Greece
Comptes Rendus. Mathématique, Tome 361 (2023) no. G9, pp. 1429-1448

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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.

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DOI : 10.5802/crmath.480

Dalezios, Georgios 1 ; Emmanouil, Ioannis 2

1 Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
2 Department of Mathematics, University of Athens, Athens 15784, Greece
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Homological dimension based on a class of {Gorenstein} flat modules},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1429--1448},
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Dalezios, Georgios; Emmanouil, Ioannis. Homological dimension based on a class of Gorenstein flat modules. Comptes Rendus. Mathématique, Tome 361 (2023) no. G9, pp. 1429-1448. doi: 10.5802/crmath.480

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