2023/09/05 by Jian Liu, Wei Ren, Liu, Jian +1
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2309.02372
openalex publication_date 2023/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let φ\colon R→ A be a ring homomorphism, where R is a commutative noetherian ring and A is a finite R-algebra. We provide criteria for detecting the ascent and descent of Gorenstein homological properties. %As an application, one can deduce a result that supports a question of Avramov and Foxby. We observe that the ascent and descent of Gorenstein homological property can detect the Gorenstein properties of rings along φ. Finally, we describe when φ induces a triangle equivalence between the stable categories of finitely generated Gorenstein projective modules over R and A.