Tilting in module categories

@inproceedings{Wisbauer2000TiltingIM,
  title={Tilting in module categories},
  author={Robert Wisbauer},
  year={2000}
}
Let M be a module over an associative ring R and σ[M ] the category of M -subgenerated modules. Generalizing the notion of a projective generator in σ[M ], a module P ∈ σ[M ] is called tilting in σ[M ] if (i) P is projective in the category of P -generated modules, (ii) every P -generated module is P presented, and (iii) σ[P ] = σ[M ]. We call P self-tilting if it is tilting in σ[P ]. Examples of (not self-small) tilting modules are I Q/ZZ in the category of torsion ZZ-modules, I Q⊕ I Q/ZZ in… CONTINUE READING

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