Cleft extensions of rings and singularity categories

Autor:	Kostas, Panagiotis
Rok vydání:	2024
Předmět:	Mathematics - Representation Theory Mathematics - Category Theory Mathematics - Rings and Algebras 16E 16E30 16E65 16E10 16G50 18E 18G80
Druh dokumentu:	Working Paper
Popis:	This paper provides a systematic treatment of Gorenstein homological aspects for cleft extensions of rings. In particular, we investigate Goresnteinness, Gorenstein projective modules and singularity categories in the context of cleft extensions of rings. This setting includes triangular matrix rings, trivial extension rings and tensor rings, among others. Under certain conditions, we prove singular equivalences between the algebras in a cleft extension, unifying an abundance of known results. Moreover, we compare the big singularity categories of cleft extensions of rings in the sense of Krause. Comment: 47 pages, version 2: minor changes in Section 7, comments are welcome
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2409.07919 Zobrazit plný text záznamu View this record from Arxiv