Papers by Juan Luis Elías
arXiv (Cornell University), Feb 20, 2003
Let R be a Cohen-Macaulay local ring with maximal ideal m. In this paper we present a procedure f... more Let R be a Cohen-Macaulay local ring with maximal ideal m. In this paper we present a procedure for computing the Ratllif-Rush closure of a m−primary ideal I ⊂ R.
Contemporary Mathematics, 1994
Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting fo... more Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy an article for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication (including abstracts) is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Manager of Editorial Services, American Mathematical Society,
Michigan Mathematical Journal, 2008
Journal of Pure and Applied Algebra, 1991
We prove that, given a local Cohen-Macaulay ring (A, m). suitable relations between the first two... more We prove that, given a local Cohen-Macaulay ring (A, m). suitable relations between the first two coefficients of the Hilbert polynomial determine the whole Hilbert function of A. The connection of these ideas with the Cohen-Macaulayness of the associated graded ring is also considered.
Proceedings of the American Mathematical Society, 2014
In this paper we consider Artin compressed local algebras, that is, local algebras with maximal l... more In this paper we consider Artin compressed local algebras, that is, local algebras with maximal length in the class of those with given embedding dimension and socle type. They have been widely studied by several authors, including Boij, Iarrobino, Fröberg and Laksov. In this class the Gorenstein algebras play an important role. The authors proved that a compressed Gorenstein K-algebra of socle degree 3 is canonically graded, i.e. analytically isomorphic to its associated graded ring. This unexpected result has been extended to compressed level K-algebras of socle degree 3 in a paper by De Stefani. This paper somehow concludes the investigation proving that Artin compressed Gorenstein K-algebras of socle degree s ≤ 4 are always canonically graded, but explicit examples prove that the result does not extend to socle degree 5 or to compressed level K-algebras of socle degree 4 and type > 1. As a consequence of this approach we present classes of Artin compressed K-algebras which are canonically graded.
Nagoya Mathematical Journal, 1991
Let I be a homogeneous ideal of a polynomial ring over a field, v(I) the number of elements of an... more Let I be a homogeneous ideal of a polynomial ring over a field, v(I) the number of elements of any minimal basis of I, e = e(I) the multiplicity or degree of R/I, h = h(I) the height or codimension of I, i = indeg (I) the initial degree of J, i.e. the minimal degree of non zero elements of I.This paper is mainly devoted to find bounds for v(I) when I ranges over large classes of ideals. For instance we get bounds when I ranges over the set of perfect ideals with preassigned codimension and multiplicity and when I ranges over the set of perfect ideals with preassigned codimension, multiplicity and initial degree. Moreover all the bounds are sharp since they are attained by suitable ideals. Now let us make some historical remarks.
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2006
Let R be a Cohen–Macaulay local ring, and let I ⊂ R be an ideal with minimal reduction J. In this... more Let R be a Cohen–Macaulay local ring, and let I ⊂ R be an ideal with minimal reduction J. In this paper we attach to the pair (I, J) a non-standard bigraded module ΣI, J. The study of the bigraded Hilbert function of ΣI, J allows us to prove an improved version of Wang's conjecture and a weak version of Sally's conjecture, both on the depth of the associated graded ring grI(R). The module ΣI, J can be considered as a refinement of the Sally module introduced previously by Vasconcelos.
Proceedings of the American Mathematical Society, 2008
In this note we compute the Poincaré series of almost stretched Gorenstein local rings. It turns ... more In this note we compute the Poincaré series of almost stretched Gorenstein local rings. It turns out that it is rational.
Journal of Pure and Applied Algebra, 1996
Let (A, m) be Cohen-Macaulay local ring with maximal ideal m and dimension d. It is well known th... more Let (A, m) be Cohen-Macaulay local ring with maximal ideal m and dimension d. It is well known that for II 9 0, the length of the A-module A/m" is given by The integers paper an e, are called the Hilbert coefficients of A. In this paper an upper bound is given for e2 in terms of e,, P, and the embedded codimension h of A. If d I 2 and the bound is reached, A has a specified Hilbert function. Similarly, in the one-dimensional case, we study the extremal behaviour with respect to the known inequality This implies that e!" = e!i+l). , going on in this way, we see that eji' does not depend on i, so that we can hrite fkr every i 2 0 d+i-1
Journal of Algebra, 2014
The Hilbert function of standard graded algebras are well understood by Macaulay's theorem and ve... more The Hilbert function of standard graded algebras are well understood by Macaulay's theorem and very little is known in the local case, even if we assume that the local ring is a complete intersection. An extension to the power series ring R of the theory of Gröbner bases (w.r.t. local degree orderings) enable us to characterize the Hilbert function of one dimensional quadratic complete intersections A = R/I, and we give a structure theorem of the minimal system of generators of I in terms of the Hilbert function. We find several restrictions for the Hilbert function of A in the case that I is a complete intersection of type (2, b). Conditions for the Cohen-Macaulyness of the associated graded ring of A are given.
Journal of Algebra, 2009
In this paper we study some cohomological properties of non-standard multigraded modules and Vero... more In this paper we study some cohomological properties of non-standard multigraded modules and Veronese transforms of them. Among others numerical characters, we study the generalized depth of a module and we see that it is invariant by taking a Veronese transform. We prove some vanishing theorems for the local cohomology modules of a multigraded module; as a corollary of these results we get that the depth of a Veronese module is asymptotically constant.
Communications in Algebra, 2013
Let K be an algebraically closed field of characteristic 0, and let A be an Artinian Gorenstein l... more Let K be an algebraically closed field of characteristic 0, and let A be an Artinian Gorenstein local commutative and Noetherian K-algebra, with maximal ideal m. In the present paper we prove a structure theorem describing such kind of K-algebras satisfying m 4 = 0. We use this result in order to prove that such a K-algebra A has rational Poincaré series and it is always smoothable in any embedding dimension, if dim K m 2 /m 3 ≤ 4. We also prove that the generic Artinian Gorenstein local K-algebra with socle degree three has rational Poincaré series, in spite of the fact that such algebras are not necessarily smoothable.
Communications in Algebra, 2011
The aim of this paper is to establish, among other results, the asymptotic stability of the depth... more The aim of this paper is to establish, among other results, the asymptotic stability of the depth of the graded pieces of a non-standard multigraded module. As a corollary we get the asymptotic stability of the depth of the graded pieces of the multigraded Rees algebra defined by a finite set of ideals and their associated multigraded rings.
Algebras and Representation Theory, 2009
In this paper we attack the problem of the classification, up to analytic isomorphism, of Artinia... more In this paper we attack the problem of the classification, up to analytic isomorphism, of Artinian Gorenstein local k-algebras with a given Hilbert Function. We solve the problem in the case the square of the maximal ideal is minimally generated by two elements and the socle degree is high enough.
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Papers by Juan Luis Elías