Gorenstein projective modules and recollements over triangular matrix rings

摘要

Letbe a triangular matrix ring withRandSrings andanR-S-bimodule. We describe Gorenstein projective modules overT. In particular, we refine a result of Enochs, Cortes-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 ofrestricts to a recollement of its subcategoryconsisting of complexes with finite Gorenstein projective dimension. As applications, we obtain recollements of the stable categoryand recollements of the Gorenstein defect category