Publikace na Matematicko-fyzikální fakulta |
2014
Abstrakt
Recently, tilting and cotilting classes over commutative Noetherian rings have been classified. 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.