21 research outputs found
Emmy Noether i l’àlgebra commutativa
Emmy Noether representa un punt d’inflexió fonamental en el desenvolupament de l’Àlgebra Commutativa. Per una banda, en ella
conflueixen algunes de les línies evolutives prèvies més importants. Per altra, a partir del seu treball i, sobretot, de la influència de la
seva manera de pensar i treballar les Matemàtiques, l’Àlgebra Commutativa va prendre la volada necessària per convertir-se en una
àrea de recerca amb gran vitalitat. A la xerrada revisarem aquesta evolució centrant-nos en el paper exercit per Emmy Noether en el
procés, tot explicant alguns dels seus resultats.La Factoria FM
On the Apery sets of monomial curves
In this paper, we use the Ap\'ery table of the numerical semigroup associated
to an affine monomial curve in order to characterize arithmetic properties and
invariants of its tangent cone. In particular, we precise the shape of the
Ap\'ery table of a numerical semigroup of embedding dimension 3, when the
tangent cone of its monomial curve is Buchsbaum or 2-Buchsbaum, and give new
proofs for two conjectures raised by V. Sapko (Commun. Algebra {29}:4759-4773,
2001) and Y. H. Shen (Commun. Algebra {39}:1922-1940, 2001). We also provide a
new simple proof in the case of monomial curves for Sally's conjecture (Numbers
of Generators of Ideals in Local Rings, 1978) that the Hilbert function of a
one-dimensional Cohen-Macaulay ring with embedding dimension three is
non-decreasing. Finally, we obtain that monomial curves of embedding dimension
4 whose tangent cones are Buchsbaum, and also monomial curves of any embedding
dimensions whose numerical semigroups are balanced, have non-decreasing Hilbert
functions. Numerous examples are provided to illustrate the results, most of
them computed by using the NumericalSgps package of GAP (Delgado et al.,
NumericalSgps-a GAP package, 2006).Comment: To appear in Semigroup Foru
On some local cohomology spectral sequences
We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The 1st type of spectral sequences involves the left derived functors of the colimit of the direct system that we obtain by applying a family of functors to a single module. For the 2nd type we follow a completely different strategy as we start with the inverse system that we obtain by applying a covariant functor to an inverse system. The spectral sequences involve the right derived functors of the corresponding limit. We also have a version for contravariant functors. In all the introduced spectral sequences we provide sufficient conditions to ensure their degeneration at their 2nd page. As a consequence we obtain some decomposition theorems that greatly generalize the well-known decomposition formula for local cohomology modules of Stanley–Reisner rings given by Hochster.Peer ReviewedPostprint (author's final draft
The safe use of N_2, CO_2 and CO_2/N_2 cylinders in the beverage dispense industry
Includes bibliographical referencesAvailable from British Library Document Supply Centre- DSC:3292. 776(32) / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo