For a locally presentable abelian category B with projective generator, we construct the derived and contraderived model structures on of complexes, proving in particular existence enough homotopy complexes objects. We also show that D(B) is generated, as triangulated coproducts, by generator B. Grothendieck A, injective coderived complexes. Assuming Vopěnka's principle, prove D(A) products, co...

In this paper we revisit the problem of determining when heart a t-structure is Grothendieck category, with special attention to case Happel-Reiten-Smalo (HSR) in derived category associated torsion pair latter. We HRS tilting process deriving from it lot information on t-structures which have projective generator or an injective cogenerator, and obtain several bijections between classes pairs ...

For a finite dimensional algebra A over an algebraically closed field, let T (A) denote the trivial extension of A by its minimal injective cogenerator bimodule. We prove that, if TA is a tilting module and B = EndTA, then T (A) is tame if and only if T (B) is tame. Introduction. Let k be an algebraically closed field. In this paper, an algebra A is always assumed to be associative, with an ide...

The cluster category was introduced in (BMRRT, 2006) and also in (CCS1, 2006) for type A, as a categorical model to understand better the cluster algebras of Fomin and Zelevinsky (FZ, 2002). It is a quotient of the bounded derived category Db(modA) of the finitely generated modules over a finite dimensional hereditary algebra A. It was then natural to consider the endomorphism algebras of tilti...

A module M is called epi-retractable if every submodule of M is a homomorphic image of M. Dually, a module M is called co-epi-retractable if it contains a copy of each of its factor modules. In special case, a ring R is called co-pli (resp. co-pri) if RR (resp. RR) is co-epi-retractable. It is proved that if R is a left principal right duo ring, then every left ideal of R is an epi-retractable ...

a module m is called epi-retractable if every submodule of m is a homomorphic image of m. dually, a module m is called co-epi-retractable if it contains a copy of each of its factor modules. in special case, a ring r is called co-pli (resp. co-pri) if rr (resp. rr) is co-epi-retractable. it is proved that if r is a left principal right duo ring, then every left ideal of r is an epi-retractable ...

In this paper we study the notions of cogenerator and subdirectlyirreducible in the category of S-poset. First we give somenecessary and sufficient conditions for a cogenerator $S$-posets.Then we see that under some conditions, regular injectivityimplies generator and cogenerator. Recalling Birkhoff'sRepresentation Theorem for algebra, we study subdirectlyirreducible S-posets and give this theo...