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Seminario MALGA Padova Verona - Moduli Algebre Anelli

Martedi' 22 Giugno 2010 - J. Saroch, L. Angeleri

ARGOMENTI: Seminari

Martedi' 22 giugno 2010 - Aula 2AB45 Torre Archimede

ore 15:00
Jan Saroch (Charles University Prague)
"Approximation properties of the class of Mittag-Leffler modules"

-Abstract
Some recent results concerning the class D of all flat Mittag-Leffler modules will be presented. In particular, it will be shown that D is always a Kaplansky class, although it is never deconstructible (unless we are working over a right perfect ring); the latter, much harder result is due to Jan Trlifaj and Dolors Herbera. Further, the possibility of D being a precovering class will be discussed. Here, the conjecture is, again, that it can happen only over a right perfect ring. Some particular results and a conceivable strategy for general solution will be presented. This is a joint work with Jan Trlifaj.

ore 16:30
Lidia Angeleri (Universita' di Verona)
"Auslander-Reiten-components over pure-semisimple hereditary rings"

-Abstract
I will report on joint work with Dolors Herbera. We study the representation type of a hereditary, indecomposable, left pure semisimple ring in terms of properties of a certain tilting and cotilting module W. In particular, we apply the tilting and the cotilting functors to describe the Auslander-Reiten-components of the endomorphism ring of W. I will close the talk with a list of open questions.

Rif. int. S. Bazzoni

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