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On stable equivalences of module subcategories over a semiperfect noetherian ring

100%

Kameyama N., Kimura Y., Nishida K.

Colloquium Mathematicum

2014

tom 137

nr 1

7-26

Given a semiperfect two-sided noetherian ring Λ, we study two subcategories $𝓐_k(Λ) = {M ∈ mod Λ | Ext_{Λ}^{j}(Tr M,Λ) = 0 (1 ≤ j ≤ k)}$ and $𝓑_k(Λ) = {N ∈ mod Λ | Ext_{Λ}^{j}(N,Λ) = 0 (1 ≤ j ≤ k)}$ 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 $𝓐_{k}(Λ)$ and $𝓑_{k}(Λ)$, 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

100%

Hoshino M., Kameyama N., Koga H.

Colloquium Mathematicum

2015

tom 141

nr 1

1-11

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.

Ograniczanie wyników

2 Colloquium Mathematicum

2 Kameyama N.

1 Hoshino M.

1 Kimura Y.

1 Koga H.

1 Nishida K.

1 2015

1 2014

Wyniki wyszukiwania

On stable equivalences of module subcategories over a semiperfect noetherian ring

Construction of Auslander-Gorenstein local rings as Frobenius extensions