On the structure of Noetherian symbolic Rees Algebras.
Let be a field and be the standard bigraded polynomial ring over . In this paper, we explicitly describe the structure of finitely generated bigraded “sequentially Cohen-Macaulay” -modules with respect to . Next, we give a characterization of sequentially Cohen-Macaulay modules with respect to in terms of local cohomology modules. Cohen-Macaulay modules that are sequentially Cohen-Macaulay with respect to are considered.
In this note we give a description of a morphism related to the structure of the canonical model of the Rees algebra R(I) of an ideal I in a local ring. As an application we obtain Ikeda's criteria for the Gorensteinness of R(I) and a result of Herzog-Simis-Vasconcelos characterizing when the canonical module of R(I) has the expected form.
Let be a standard graded -algebra over a field . Then can be written as , where is a graded ideal of a polynomial ring . Assume that and is a strongly stable monomial ideal. We study the symmetric algebra of the first syzygy module of . When the minimal generators of are all of degree 2, the dimension of is calculated and a lower bound for its depth is obtained. Under suitable conditions, this lower bound is reached.
We describe an ultrametric version of the Stone-Weierstrass theorem, without any assumption on the residue field. If is a subset of a rank-one valuation domain , we show that the ring of polynomial functions is dense in the ring of continuous functions from to if and only if the topological closure of in the completion of is compact. We then show how to expand continuous functions in sums of polynomials.
Let be a proper ideal of a commutative Noetherian ring R of prime characteristic p and let Q() be the smallest positive integer m such that , where is the Frobenius closure of . This paper is concerned with the question whether the set is bounded. We give an affirmative answer in the case that the ideal is generated by an u.s.d-sequence c₁,..., cₙ for R such that (i) the map induced by multiplication by c₁...cₙ is an R-monomorphism; (ii) for all , c₁/1,..., cₙ/1 is a -filter regular sequence...
In 2000 A. Alesina and M. Galuzzi presented Vincent’s theorem “from a modern point of view” along with two new bisection methods derived from it, B and C. Their profound understanding of Vincent’s theorem is responsible for simplicity — the characteristic property of these two methods. In this paper we compare the performance of these two new bisection methods — i.e. the time they take, as well as the number of intervals they examine in order to isolate the real roots of polynomials — against that...
In this paper, we define Gorenstein injective rings, Gorenstein injective modules and their envelopes. The main topic of this paper is to show that if is a Gorenstein integral domain and is a left -module, then the torsion submodule of Gorenstein injective envelope of is also Gorenstein injective. We can also show that if is a torsion -module of a Gorenstein injective integral domain , then the Gorenstein injective envelope of is torsion.