Gorenstein homology, relative pure homology and virtually Gorenstein\n rings

2014/03/05 by Fatemeh Zareh-Khoshchehreh, Mohsen Asgharzadeh, Zareh-Khoshchehreh, Fatemeh +3 · 1 citation
Mathematics · Medicine · #13C13 #13D02 #13D05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Intracranial Aneurysms: Treatment and Complications

paper · pdf · doi:10.48550/arxiv.1403.1155

openalex publication_date 2014/03/05 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

We consider the following question: Is Gorenstein homology a X-pure homology,\nin the sense defined by Warfield, for a class X of modules? Let GP denote the\nclass of Gorenstein projective modules. We prove that over a commutative\nNoetherian ring R of finite Krull dimension, Gorenstein homology is a GP-pure\nhomology if and only if R is virtually Gorenstein.\n

Citations

• Stable module theory
• Acyclicity versus total acyclicity for complexes over noetherian rings

Cited by

• On local rings of finite syzygy representation type

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