Seminario Dottorato: Injective modules and Star operations

Wednesday 18 November 2009 - Gabriele Fusacchia

ARGOMENTI: Seminari Dottorato

Wednesday 18 November 2009 h. 15:00, room 2AB/40
Gabriele Fusacchia (Univ. Padova, Dip. Mat.)
"Injective modules and Star operations"

The problem of classifying injective modules in terms of direct decompositions does not admit, in general, a solution. Exhaustive results have been obtained, however, when restricting to special classes of domains, such as Prufer domains, valuation domains and Noetherian domains. After recalling some basic notions on injective modules and direct decompositions, we provide examples of domains in which the classification is not possible, and we give the classical results on valuation and Noetherian domains. Next we introduce the notion of star operation over a domain, a special kind of closure operator defined over the fractional ideals. Thanks to this concept, we show how the classification on Noetherian domains can be generalized, allowing to completely classify special subclasses of injective modules over domains which are not Noetherian.

Rif. int. C. Marastoni, T. Vargiolu, M. Dalla Riva

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