-Gorenstein projective dimensions
Z Zhao, X Xu - arXiv preprint arXiv:1801.09127, 2018 - arxiv.org
… all projective R-modules) are denoted by … projective dimension and Gorenstein projective
dimension of M. We always assume that X is a class of R-modules which contains all projective …
dimension of M. We always assume that X is a class of R-modules which contains all projective …
Gorenstein Objects in Extriangulated Categories
Z He - arXiv preprint arXiv:2011.14552, 2020 - arxiv.org
… projective resolution and ξ-Gprojective resolution for any object A in C. What is more, we define
a particular ξGorenstein projective … of G-dimension zero modules, and dually they defined …
a particular ξGorenstein projective … of G-dimension zero modules, and dually they defined …
Relative singularity categories and Gorenstein‐projective modules
XW Chen - Mathematische Nachrichten, 2011 - Wiley Online Library
… We prove that for a Gorenstein ring, the stable category of Gorenstein-projective modules
is … has finite projective dimension. Thus we infer that K has finite projective dimension. Note …
is … has finite projective dimension. Thus we infer that K has finite projective dimension. Note …
The cotorsion pair generated by the Gorenstein projective modules and -pure-injective modules
M Cortés-Izurdiaga, J Šaroch - arXiv preprint arXiv:2104.08602, 2021 - arxiv.org
… Recall that a ring R is called right Gorenstein regular [9] if the classes of modules with finite
projective dimension and with finite injective dimension coincide. Moreover, a duality pair is a …
projective dimension and with finite injective dimension coincide. Moreover, a duality pair is a …
Finiteness of Gorenstein injective dimension of modules
… s G-dimension extends the notion of projective dimension, and its finiteness characterizes
Gorenstein … In particular, if T has finite projective dimension over Rp, we can conclude that Ext i …
Gorenstein … In particular, if T has finite projective dimension over Rp, we can conclude that Ext i …
Modules with finite reducing Gorenstein dimension
T Araya, O Celikbas, J Cook, T Kobayashi - Beiträge zur Algebra und …, 2024 - Springer
… (M)\), in case M is an R-module and \(x\in \mathfrak {m}\) is a non zero-divisor on R and M. …
,}}_R(M)\) in case M is an R-module and \(x\in \mathfrak {m}\) is a non zero-divisor on R and M, …
,}}_R(M)\) in case M is an R-module and \(x\in \mathfrak {m}\) is a non zero-divisor on R and M, …
A short note on deformations of (strongly) Gorenstein-projective modules over the dual numbers
JA Vélez-Marulanda, H Suárez - São Paulo Journal of Mathematical …, 2024 - Springer
… \(\Lambda\)-modules are also known in the literature as modules of Gorenstein dimension
zero or totally reflexive (see [1, 5, §2]). We denote by \(\Lambda\)-Gproj the category of …
zero or totally reflexive (see [1, 5, §2]). We denote by \(\Lambda\)-Gproj the category of …
The Gorenstein defect category
PA Bergh, S Oppermann… - The Quarterly Journal of …, 2015 - academic.oup.com
… every finitely generated module has finite Gorenstein dimension are precisely the Gorenstein
rings. … ideal |$\mathfrak n=(x,y,z)$|, embedding dimension 3, Loewy length 3 and length 6. …
rings. … ideal |$\mathfrak n=(x,y,z)$|, embedding dimension 3, Loewy length 3 and length 6. …
Gorenstein homological dimensions for extriangulated categories
J Hu, D Zhang, P Zhou - Bulletin of the Malaysian Mathematical Sciences …, 2021 - Springer
… Gorenstein projective dimension of a ring R is equal to the global Gorenstein injective
dimension … Ren and Liu in [14] studied Gorenstein homological dimensions for triangulated …
dimension … Ren and Liu in [14] studied Gorenstein homological dimensions for triangulated …
Testing for the Gorenstein property
O Celikbas, S Sather-Wagstaff - Collectanea mathematica, 2016 - Springer
… ring \((R,\mathfrak m)\) is Gorenstein if and only if it admits an … (\mathfrak m\)-primary ideal of
finite Gorenstein dimension. This … Gorenstein dimension, but not that of projective dimension. …
finite Gorenstein dimension. This … Gorenstein dimension, but not that of projective dimension. …
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