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On weak i -homotopy equivalences of modules

Zheng-Xu He (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si definisce il gruppo di i —omotopia di un singolo modulo e si introduce la nozione di equivalenza i -omotopica debole. Sotto determinate condizioni per l'anello di base Λ oppure per i moduli considerati, le equivalenze i -omotopiche deboli coincidono con le equivalenze i -omotopiche (forti).

One-sided Gorenstein subcategories

Weiling Song, Tiwei Zhao, Zhaoyong Huang (2020)

Czechoslovak Mathematical Journal

We introduce the right (left) Gorenstein subcategory relative to an additive subcategory 𝒞 of an abelian category 𝒜 , and prove that the right Gorenstein subcategory r 𝒢 ( 𝒞 ) is closed under extensions, kernels of epimorphisms, direct summands and finite direct sums. When 𝒞 is self-orthogonal, we give a characterization for objects in r 𝒢 ( 𝒞 ) , and prove that any object in 𝒜 with finite r 𝒢 ( 𝒞 ) -projective dimension is isomorphic to a kernel (or a cokernel) of a morphism from an object in 𝒜 with finite 𝒞 -projective dimension...

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