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Currently displaying 1 – 2 of 2

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On stable equivalences of module subcategories over a semiperfect noetherian ring

Noritsugu Kameyama; Yuko Kimura; Kenji Nishida — 2014

Colloquium Mathematicae

Given a semiperfect two-sided noetherian ring Λ, we study two subcategories $_{k} (Λ) = M \in m o d Λ | E x t_{Λ}^{j} (T r M, Λ) = 0 (1 \leq j \leq k)$ and $_{k} (Λ) = N \in m o d Λ | E x t_{Λ}^{j} (N, Λ) = 0 (1 \leq j \leq k)$ of the category mod Λ of finitely generated right Λ-modules, where Tr M is Auslander’s transpose of M. In particular, we give another convenient description of the categories $_{k} (Λ)$ and $_{k} (Λ)$ , and we study category equivalences and stable equivalences between them. Several results proved in [J. Algebra 301 (2006), 748-780] are extended to the case when Λ is a two-sided noetherian semiperfect ring.

Construction of Auslander-Gorenstein local rings as Frobenius extensions

Mitsuo Hoshino; Noritsugu Kameyama; Hirotaka Koga — 2015

Colloquium Mathematicae

Starting from an arbitrary ring R we provide a systematic construction of ℤ/nℤ-graded rings A which are Frobenius extensions of R, and show that under mild assumptions, A is an Auslander-Gorenstein local ring if and only if so is R.

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