When are definable classes tilting and cotilting classes? |
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Authors: | Silvana Bazzoni |
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Institution: | aDipartimento di Matematica Pura e Applicata, Università di Padova, Via Trieste 63, 35121 Padova, Italy |
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Abstract: | It is known that tilting classes are of finite type, while cotilting classes are not always of cofinite type. We investigate this phenomenon. By using a bijection between definable classes of left modules and definable classes of right modules, we prove that it reflects the asymmetry existing between the notions of covers and envelopes or, otherwise stated, right and left approximations.In particular we show that there exist definable torsion classes containing the injective modules which are not tilting classes. |
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Keywords: | Tilting and cotilting classes Definable classes Precovers and preenvelopes Functor categories |
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