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Trivial Maximal 1Orthogonal Subcategories For Auslander’s 1Gorenstein Algebras
, 2009
"... Let Λ be an Auslander’s 1Gorenstein Artinian algebra with global dimension 2. If Λ admits a trivial maximal 1orthogonal subcategory of mod Λ, then for any indecomposable module M ∈ mod Λ, we have that the projective dimension of M is equal to 1 if and only if so is its injective dimension and th ..."
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Let Λ be an Auslander’s 1Gorenstein Artinian algebra with global dimension 2. If Λ admits a trivial maximal 1orthogonal subcategory of mod Λ, then for any indecomposable module M ∈ mod Λ, 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.