Browsing by Subject "Commutative algebra"
Now showing items 120 of 22

A Koszul complex over skew polynomial rings
(20190101)
Article
Open AccessWe construct a Koszul complex in the category of left skew polynomial rings associated with a flat endomorphism that provides a finite free resolution of an ideal generated by a Koszul regular sequence 
An approach to the uniform ArtinRees theorems from the notion of relation type
(2003)
Article
Open Access 
Bernstein's inequality and holonomicity for certain singular rings
(2021)
Research report
Open AccessIn this manuscript we prove the Bernstein inequality and develop the theory of holonomic Dmodules for rings of invariants of finite groups in characteristic zero, and for strongly Fregular finitely generated graded ... 
BernsteinSato functional equations, Vfiltrations, and multiplier ideals of direct summands
(2019)
Research report
Open AccessThis paper investigates the existence and properties of a Bernstein– Sato functional equation in nonregular settings. In particular, we construct Dmodules in which such formal equations can be studied. The existence of ... 
BernsteinSato polynomials in commutative algebra
(Springer Nature, 20220223)
Part of book or chapter of book
Restricted access  publisher's policyThis is an expository survey on the theory of BernsteinSato polynomials with special emphasis in its recent developments and its importance in commutative algebra 
Bernstein–Sato theory for determinantal ideals in positive characteristic
(Universitat Politècnica de Catalunya, 20230524)
Bachelor thesis
Open Access
Covenantee: University of UtahSigui R un anell de polinomis sobre un cos k. Una varietat algebraica sobre k és un conjunt de punts on s'anul·len alguns polinomis de R. Amb la finalitat d'estudiar aquestes varietats i les seves singularitats, una pràctica ... 
Dmodules, BernsteinSato polynomials and Finvariants of direct summands
(20171201)
Article
Open AccessWe study the structure of D modules over a ring R which is a direct sum mand of a polynomial or a power series ring S with coefficients over a field. We relate properties of D modules over R to D modules over S . We ... 
Divisors of expected Jacobian type
(2021)
Article
Open AccessDivisors whose Jacobian ideal is of linear type have received a lot of attention recently because of its connections with the theory of Dmodules. In this work we are interested on divisors of expected Jacobian type, that ... 
Emmy Noether i l’àlgebra commutativa
(20090218)
Audiovisual
Open AccessEmmy 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 ... 
Finiteness properties of local cohomology modules
(Universitat Politècnica de Catalunya, 202209)
Master thesis
Open AccessLocal cohomology modules are one of the central objects in commutative algebra. However, the structure of these modules is still full of mystery. Lyubeznik conjectured that the number of associated primes and all the Bass ... 
Generating functions associated to Frobenius algebras
(Elsevier, 20191201)
Article
Open AccessWe introduce a generating function associated to the homogeneous generators of a graded algebra that measures how far is this algebra from being finitelygenerated. For the case of some algebras of Frobenius endomorphisms ... 
Hilbert Revisited
(20090318)
Audiovisual
Open AccessStarting with a look at Hilbert's famous 1890 paper, which was considered at one time to have dealt the deathblow to Invariant Theory, and which inluded the famous Basis Theorem and Syzygy Theorem, we will trace some ... 
Lyubeznik numbers of local rings and linear strands of graded ideals
(Springer, 2016)
Conference report
Restricted access  publisher's policyWe report recent work on the study of Lyubeznik numbers and their relation to invariants coming from the study of linear strands of free resolutions. 
Lyubeznik numbers of local rings and linear strands of graded ideals
(Springer, 2016)
Part of book or chapter of book
Restricted access  publisher's policyWe report recent work on the study of Lyubeznik numbers and their relation to invariants coming from the study of linear strands of free resolutions 
Minimal canonical comprehensive Gröbner systems
(2009)
Article
Open AccessThis is the continuation of Montes' paper "On the canonical discussion of polynomial systems with parameters''. In this paper, we define the Minimal Canonical Comprehensive Gröbner System of a parametric ideal and fix under ... 
Minimal free resolutions of lattice ideals of digraphs
(20180302)
Article
Open AccessBased upon a previous work of Manjunath and Sturmfels for a finite, complete, undirected graph, and a refined algorithm by Eröcal, Motsak, Schreyer and Steenpaß for computing syzygies, we display a free resolution of the ... 
Monomial generators of complete planar ideals
(20200101)
Article
Open AccessWe provide an algorithm that computes a set of generators for any complete ideal in a smooth complex surface. More interestingly, these generators admit a presentation as monomials in a set of maximal contact elements ... 
On the integral degree of integral ring extensions
(20190201)
Article
Open AccessLet A ¿ B be an integral ring extension of integral domains with fields of fractions K and L, respectively. The integral degree of A ¿ B, denoted by dA(B), is defined as the supremum of the degrees of minimal integral ... 
Positivity properties of relative complete intersections
(201410)
Research report
Open AccessWe give conditions for fpositivity of relative complete intersections in projective bundles. We also derive an instability result for the fibres. 
Rational parameterizations approach for solving equations in some dynamical systems problems
(201908)
Article
Open AccessWe show how the use of rational parameterizations facilitates the study of the number of solutions of many systems of equations involving polynomials and square roots of polynomials. We illustrate the effectiveness of this ...