2009/03/04 by Zhaoyong Huang, Huang, Zhaoyong, Xiaojin Zhang +1 · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.0903.0762
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 ∈ \mod Λ, 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 that Λ is a tilted algebra.