By analogy with the projective, injective and flat modules, in this paper we study some properties of -Gorenstein projective, injective and flat modules and discuss some connections between -Gorenstein injective and -Gorenstein flat modules. We also investigate some connections between -Gorenstein projective, injective and flat modules of change of rings.
One gives a formula for the calculation of the local intersection multiplicity index of analytic varieties, analogous to the Bézout formula in the case of algebraic varieties in the projective space, in the case of normal crossings. One obtains also a recurrent process for the calculation of the local intersection multiplicity index of plane analytic curves.
We introduce in this article a new method to calculate all absolute and relatif primitive invariants of finite groups. This method is inspired from K. Girstmair which calculate an absolute primitive invariant of minimal degree. Are presented two algorithms, the first one enable us to calculate all primitive invariants of minimal degree, and the second one calculate all absolute or relative primitive invariants with distincts coefficients. This work take place in Galois Theory and Invariant Theory. ...
Let be a non-maximal order in a finite algebraic number field with integral closure . Although is not a unique factorization domain, we obtain a positive integer and a family (called a Cale basis) of primary irreducible elements of such that has a unique factorization into elements of for each coprime with the conductor of . Moreover, this property holds for each nonzero when the natural map is bijective. This last condition is actually equivalent to several properties linked...
For a finite Coxeter group and a Coxeter element of ; the -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of . Its maximal cones are naturally indexed by the -sortable elements of . The main result of this paper is that the known bijection cl between -sortable elements and -clusters induces a combinatorial isomorphism of fans. In particular, the -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for . The rays...
The postulation of Aritméticamente Cohen-Macaulay (ACM) subschemes of the projective space PkN is well known in the case of codimension 2. There are many different ways of recording this numerical information: numerical character of Gruson/Peskine, h-vector, postulation character of Martin-Deschamps/Perrin... The first aim of this paper is to show the equivalence of these notions. The second and most important aim, is to study the postulation of codimension 3 ACM subschemes of PN. We use a result...
The Castelnuovo-Mumford regularity reg(M) is one of the most important invariants of a finitely generated graded module M over a polynomial ring R. For instance, it measures the amount of computational resources that working with M requires. In general one knows that the regularity of a module can be doubly exponential in the degrees of the minimal generators and in the number of the variables. On the other hand, in many situations one has or one conjectures a much better behavior. One may ask,...