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arXiv · 1306.6788

Cotilting modules over commutative noetherian rings

Jan Stovicek·Jan Trlifaj·Dolors Herbera
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Abstract

Recently, tilting and cotilting classes over commutative noetherian rings have been classified in arXiv:1203.0907. We proceed and, for each n-cotilting class C, construct an n-cotilting module inducing C by an iteration of injective precovers. A further refinement of the construction yields the unique minimal n-cotilting module inducing C. Finally, we consider localization: a cotilting module is called ample, if all of its localizations are cotilting. We prove that for each 1-cotilting class, there exists an ample cotilting module inducing it, but give an example of a 2-cotilting class which fails this property.

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Jan Stovicek, Jan Trlifaj, Dolors Herbera. 2013-06-28. Cotilting modules over commutative noetherian rings. https://doi.org/10.1016/j.jpaa.2014.01.008

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