Virtually Gorenstein rings and relative homology of complexes |
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| Affiliation: | 1. School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China;2. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, China;3. Department of Mathematics, Northwest Normal University, Lanzhou 730070, China;1. Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile;2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico;1. Department of Mathematics, China Jiliang University, Hangzhou 310018, Zhejiang Province, PR China;2. Department of Mathematics, Nanjing University, Nanjing 210093, Jiangsu Province, PR China;1. Sistiana Mare 56, 34011 Trieste, Italy;2. Departamento de Matemáticas, Universidad de La Serena, Cisternas 1200, 1700000 La Serena, Chile;3. IMUV, Universidad de Valparaíso, Gran Bretaña 1111, 2340000 Valparaíso, Chile |
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| Abstract: | We extend the notion of virtually Gorenstein rings to the setting of arbitrary rings, and prove that all rings R of finite Gorenstein weak global dimension are virtually Gorenstein such that all Gorenstein projective R-modules are Gorenstein flat. For such a ring R, we introduce the notion of relative homology functors of complexes with respect to Gorenstein projective (resp., flat) modules, and establish a balanced and a vanishing result for the homology functor. |
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| Keywords: | Gorenstein module Relative homology Virtually Gorenstein ring |
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