4 papers
Indecomposable Injectives over the Jacobson Algebra
Riccardo Colpi, Francesca Mantese, Alberto Tonolo
Let K be any field. In this paper we give a complete list of the indecomposable left injective module over the Jacobson algebra K<X,Y | XY = 1>, i.e., the free associative K-algebr…
On tilted Giraud subcategories
Riccardo Colpi, Luisa Fiorot, Francesco Mattiello
Firstly we provide a technique to move torsion pairs in abelian categories via adjoint functors and in particular through Giraud subcategories. We apply this point in order to deve…
When an abelian category with a tilting object is equivalent to a module category
Riccardo Colpi, Francesca Mantese, Alberto Tonolo
An abelian category with arbitrary coproducts and a small projective generator is equivalent to a module category \cite{Mit}. A tilting object in a abelian category is a natural ge…
On cotilting cotorsion and torsion pairs
Riccardo Colpi, Francesca Mantese, Alberto Tonolo
In this paper we study cotorsion and torsion pairs induced by cotilting modules. We prove the existence of a strong relationship between the -pure injectivity of the cotilting m…