Partial tilting modules over m - replicated algebras ⋆
نویسنده
چکیده
Let A be a hereditary algebra over an algebraically closed field k andA(m) be them-replicated algebra of A. Given an A(m)-module T , we denote by δ(T ) the number of non isomorphic indecomposable summands of T . In this paper, we prove that a partial tilting A(m)module T is a tilting A(m)-module if and only if δ(T ) = δ(A(m)), and that every partial tilting A(m)-module has complements. As an application, we deduce that the tilting quiver KA(m) of A (m) is connected. Moreover, we investigate the number of complements to almost tilting modules over duplicated algebras.
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