Geodesic
Separating Splitting Tilting Modules and Hereditary Algebras
Canadian mathematical bulletin, Tome 30 (1987) no. 2, pp. 177-181

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Let A be a finite-dimensional algebra over an algebraically closed field. By module is meant a finitely generated right module. A module T ^ is called a tilting module if and there exists an exact sequence 0 → A^ → T' → T" → 0 with T'. T" direct sums of summands of T. Let B = End T^·T^ is called separating (respectively, splitting) if every indecomposable A-module M (respectively, B-module N) is such that either Hom^(T,M) = 0 or (respectively, N ⊗ T = 0 or . We prove that A is hereditary provided the quiver of A has no oriented cycles and every separating tilting module is splitting.
DOI : 10.4153/CMB-1987-025-3
Mots-clés : Primary 16A46, secondary 16A64, Representations of hereditary algebras, tilting modules 
Assem, Ibrahim. Separating Splitting Tilting Modules and Hereditary Algebras. Canadian mathematical bulletin, Tome 30 (1987) no. 2, pp. 177-181. doi: 10.4153/CMB-1987-025-3
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