Trivial Maximal 1 - Orthogonal Subcategories For Auslander ’ s 1 - Gorenstein Algebras ∗ †
نویسندگان
چکیده
Let Λ be an Auslander’s 1-Gorenstein Artinian algebra with global dimension 2. If Λ admits a trivial maximal 1-orthogonal subcategory of modΛ, then for any indecomposable module M ∈ modΛ, we have that the projective dimension of M is equal to 1 if and only if so is its injective dimension and that M is injective if the projective dimension of M is equal to 2, which implies that Λ is almost hereditary.
منابع مشابه
Ju n 20 09 Trivial Maximal 1 - Orthogonal Subcategories For Auslander ’ s 1 - Gorenstein Algebras
Let Λ be an Auslander’s 1-Gorenstein Artinian algebra with global dimension two. If Λ admits a trivial maximal 1-orthogonal subcategory of modΛ, then for any indecomposable module M ∈ modΛ, we have that the projective dimension of M is equal to one if and only if so is its injective dimension and that M is injective if the projective dimension of M is equal to two. In this case, we further get ...
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