Infinitely generated tilting modules of finite projective dimension

A characterization of n-cotilting and n-tilting modules

We relate the theory of envelopes and covers to tilting and cotilting theory, for (infinitely generated) modules over arbitrary rings Our main result characterizes tilting torsion classes as the pretorsion classes providing special preenvelopes for all modules A dual characterization is proved for cotilting torsion-free classes using the new notion of a cofinendo module We also construct unique representing modules for these classes

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Tilting Preenvelopes and Cotilting Precovers

Quasi-Tilting Modules and Counter Equivalences

We define the notion of an infinitely generated tilting object of infinite homological dimension in an abelian category. A one-to-one correspondence between $\infty$-tilting objects in complete, cocomplete abelian categories with an injective cogenerator and $\infty$-cotilting objects in complete, cocomplete abelian categories with a projective generator is constructed. We also introduce $\infty$-tilting pairs, consisting of an $\infty$-tilting object and its $\infty$-tilting class, and obtain a bijective correspondence between $\infty$-tilting and $\infty$-cotilting pairs. Finally, we discuss the related derived equivalences and t-structures.

Infinity-tilting theory

In this paper we construct pseudo projective modules which are not quasi projective over non-commutative perfect rings. To do it we construct finite dimensional quiver algebras over the field $\mathbb{Z}_2$. The modules which are constructed will have finite length three and only three nonzero proper submodules.

/pdf/pseudo-projective-modules-which-are-not-quasi-projective-and-4zkayxj3d6.pdf

Pseudo Projective Modules Which are not Quasi Projective and Quivers

We investigate reasonably large modules with a tilting-type behaviour, regarded as bounded complexes of projective modules.

On partial tilting modules and bounded complexes

Algebras with few ∗-modules

https://link.springer.com/content/pdf/10.1007%2Fs00283-017-9733-y.pdf

Gabriella D'Este

Papers

Quasi-Tilting Modules and Counter Equivalences

Pseudo Projective Modules Which are not Quasi Projective and Quivers

On partial tilting modules and bounded complexes

Algebras with few ∗-modules

Tilting Theory: A Gift of Representation Theory to Mathematics