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[Marcelo Lanzilotta]

Finalizando el curso de Álgebra Homológica 2010 exponen Javier Cóppola e 
Ignacio Monteverde (durante el curso han expuesto temas tan interesantes 
como estos y en excelente nivel: Gabriel Núñez, Juan Pablo Lago y Bruno 
Stonek).


I charla, Martes 7 de diciembre, 10hs. Salón de Seminarios CMAT: "On the 
dimension of modules and algebras (III), Global diemnsion"; Maurice 
Auslander, 1955 (parte de este artículo).

http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.nmj/1118799684

Expone Javier Cóppola.

The terminology is that of Cartan-Eilenberg's "Homological algebra 
[Princeton, 1956]. Let R be a ring with 1, and assume that 1 operates as 
the identity map on all R-modules considered. It is shown first that the 
(left or right) global dimension of R (i.e., the supremum of the 
projective dimensions of all R-modules) is the supremum of the projective 
dimensions of the cyclic R-modules and, if R is not semisimple, exceeds 
the supremum of the projective dimensions of the ideals of R by exactly 1.
The weak global dimension of R is defined as the largest integer n (or 1) 
for which the functor Tor_n R does not vanish. It is shown that if R is 
(left or right) Noetherian then its (left or right) global dimension 
coincides with its weak global dimension. In particular, if R is both left 
and right Noetherian then its left and right global dimensions are equal.

Reviewed by G. P. Hochschild


II charla, Jueves 9 de diciembre, 10hs. Salón de Seminarios IMERL: Teorema 
de la Sicigia de Hilbert (o sea que dim.gl.(k[x_1,x_2, ..., x_n])=n).

(David Hilbert, Ueber die Theorie der algebraischen Formen, Königsberg, 15 
de febrero 1890, Prusia).

http://www.springerlink.com/content/g6416068831731u6/

Un trabajo que se adelanta 50 años al Álgebra Homológica (que surge en 
el entorno de 1940 -1950).

Expone Ignacio Monteverde.


Están todos invitados (con permiso de los expositores).