Gorenstein projective modules and recollements over triangular matrix rings
H Li, Y Zheng, J Hu, H Zhu - Communications in Algebra, 2020 - Taylor & Francis
H Li, Y Zheng, J Hu, H Zhu
Communications in Algebra, 2020•Taylor & FrancisAbstract Let T=(RM 0 S) be a triangular matrix ring with R and S rings and RMS an R–S-
bimodule. We describe Gorenstein projective modules over T. In particular, we refine a result
of Enochs, Cortés-Izurdiaga, and Torrecillas [Gorenstein conditions over triangular matrix
rings, J. Pure Appl. Algebra 218 (2014), no. 8, 1544-1554]. Also, we consider when the
recollement of D b (T‐Mod) restricts to a recollement of its subcategory D b (T‐Mod) fgp
consisting of complexes with finite Gorenstein projective dimension. As applications, we …
bimodule. We describe Gorenstein projective modules over T. In particular, we refine a result
of Enochs, Cortés-Izurdiaga, and Torrecillas [Gorenstein conditions over triangular matrix
rings, J. Pure Appl. Algebra 218 (2014), no. 8, 1544-1554]. Also, we consider when the
recollement of D b (T‐Mod) restricts to a recollement of its subcategory D b (T‐Mod) fgp
consisting of complexes with finite Gorenstein projective dimension. As applications, we …
Abstract
Let T=(RM0S) be a triangular matrix ring with R and S rings and an R–S-bimodule. We describe Gorenstein projective modules over T. In particular, we refine a result of Enochs, Cortés-Izurdiaga, and Torrecillas [Gorenstein conditions over triangular matrix rings, J. Pure Appl. Algebra 218 (2014), no. 8, 1544-1554]. Also, we consider when the recollement of Db(T‐Mod) restricts to a recollement of its subcategory Db(T‐Mod)fgp consisting of complexes with finite Gorenstein projective dimension. As applications, we obtain recollements of the stable category T‐GProj¯ and recollements of the Gorenstein defect category Ddef(T‐Mod).
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