… mod-R of finitely presented modules. As part of our analysis of a pure projective 1tilting module
T, we … [3], has enough pure projective modules, and (Theorem 4.6) that if T is a classical 1-…

… Ext-projective modules in tilting torsion classes in mod-A for hereditary artin algebras, and
prove … Since any endofinite module X is Σ-pure-injective (see [14, 26]) the pure embedding …

… module which will be called a complement. As a main result we show that such a partial tilting
module allows (… Since Aco is projective we conclude that Aco = X is the complement to M. …

… By a tilting module, we mean a tilting module of projective … τ-tilting module of finite projective
dimension is a tilting module. In … τ-tilting but not τ-tilting module of finite projective dimension …

… We define a partial n-tilting module P as a module of projective dimension ≤ n satisfying (E)…
Now, we will relate pure-injectivity properties of the tilting module T from 5.1 to closure …

… /Z is a tilting module in the category of torsion Z-modules (= cr[… shows how close tilting modules
are to projective generators. … in a[M] is weakly M-injective if and only if it is absolutely pure …

… module which is a projective generator for (Corollary 27). As in the classical case, the main
role here is played by partial tilting modules, though these modules … a partial tilting module P. …

… projective dimension of finitely generated modules over clustertilted algebras EndC(T )
where T is a cluster-tilting … It is well-known that all EndC(T )-modules are of the form HomC(T,M) …

… tilting modules, we refer to [6). An account for constructing tilting modules will be given in [18). …
Since there are only finitely many indecomposable projective modules, we conclude that …

… (infinite dimensional) tilting module L that generates all modules without … is -pure-injective,
and we obtain the equivalence of (3) and (5… Moreover, if C<ω consists of modules of projective …