Cotilting modules over commutative Noetherian rings

Recently, tilting and cotilting classes over commutative Noetherian rings have been classified in [2]. 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...

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Published inJournal of pure and applied algebra Vol. 218; no. 9; pp. 1696 - 1711
Main Authors Šťovíček, Jan, Trlifaj, Jan, Herbera, Dolors
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2014
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Summary:Recently, tilting and cotilting classes over commutative Noetherian rings have been classified in [2]. 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.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2014.01.008