Two-sided gluings of tilted algebras

We study the class of algebras A satisfying the property: all but at most finitely many non-isomorphic indecomposable A-modules are such that all their predecessors have projective dimension at most one, or all their successors have injective dimension at most one. Such a class includes the tilted algebras [D. Happel, C. Ringel, Trans. Amer. Math. Soc. 274 (1982) 399–443], the quasi-tilted algebras [D. Happel, I. Reiten, S. Smalø, Mem. Am. Math. Soc. 120 (1996) 575], the shod algebras [F.U. Coelho, M. Lanzilotta, Manuscripta Mathematica 100 (1999) 1–11], the weakly shod [F.U. Coelho, M. Lanzilotta, Preprint, 2001], and the left and right glued algebras [I. Assem, F.U. Coelho, J. Pure Appl. Algebra 96 (3) (1994) 225–243].