Stable equivalence for self-injective algebras and a generalization of tilting modules

Wakamatsu, Takayoshi

doi:10.1016/0021-8693(90)90055-s

Cited by 93 publications

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References 6 publications

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“…The following lemma is part (b) of [16,Lemma 2.1]. It generalizes Wakamatsu's lemma [24]. Lemma 1.4.…”

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confidence: 92%

Relative theory in subcategories

Mohamed¹

2009

Colloq. Math.

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Abstract. We generalize the relative (co)tilting theory of Auslander-Solberg in the category mod Λ of finitely generated left modules over an artin algebra Λ to certain subcategories of mod Λ. We then use the theory (relative (co)tilting theory in subcategories) to generalize one of the main result of Marcos et al. [Comm. Algebra 33 (2005)].Introduction. Let Λ be an artin algebra, and let mod Λ denote the category of finitely generated left Λ-modules. Auslander and Solberg [9, 10] developed a relative (co)tilting theory in mod Λ which is a generalization of standard (co)tilting theory [3], [12], [14], [23]. In this paper we develop a relative (co)tilting theory in extension-closed functorially finite subcategories of mod Λ.Let T be an ordinary tilting module over Λ. Then the module DT , where D is the usual duality between left and right modules, is a cotilting module

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