Abstract
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. © 2014 Elsevier B.V.
Original language | English |
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Pages (from-to) | 1696-1711 |
Journal | Journal of Pure and Applied Algebra |
Volume | 218 |
Issue number | 9 |
DOIs | |
Publication status | Published - 1 Jan 2014 |
Keywords
- Primary
- Secondary