Related papers: Homogeneous prime elements in normal two-dimension…

In this article we investigate when a homogeneous ideal in a graded ring is normal, that is, when all positive powers of the ideal are integrally closed. We are particularly interested in homogeneous ideals in an N-graded ring generated by…

This paper is partly a report on current knowledge concerning the structure of (generic) quantized coordinate rings and their prime spectra, and partly propaganda in support of the conjecture that since these algebras share many common…

Using polynomial evaluation, we give some useful criteria to answer questions about divisibility of polynomials. This allows us to develop interesting results concerning the prime elements in the domain of coefficients. In particular, it is…

In this paper, we prove that if $P$ is a homogeneous prime ideal inside a standard graded polynomial ring $S$ with $\dim(S/P)=d$, and for $s \leq d$, adjoining $s$ general linear forms to the prime ideal changes the $(d-s)$-th Hilbert…

We introduce a notion of generalized homogeneous derivations on graded rings as a natural extension of the homogeneous derivations defined by Kanunnikov. We then define gr-generalized derivations, which preserve the degrees of homogeneous…

Cox rings of normal varieties are factorially graded, i.e. homogeneous elements allow a unique decomposition into homogeneous factors. We study this property from an algebraic point of view and give a criterion which in a sense reduces it…

We consider ideals in a polynomial ring that are generated by regular sequences of homogeneous polynomials and are stable under the action of the symmetric group permuting the variables. In previous work, we determined the possible…

Let G/Q be an homogeneous variety embedded in a projective space P thanks to an ample line bundle L. Take a projective space containing P and form the cone X over G/Q, we call this a cone over an homogeneous variety. Let $\alpha$ a class of…

We give a bound on the Castelnuovo-Mumford regularity of a homogeneous ideals I, in a polynomial ring A, in terms of number of variables and the degrees of generators, when the dimension of A/I is at most two. This bound improves the one…

Let $K$ be an infinite field of characteristic $p>0$ and let $\lambda, \mu$ be partitions, where $\mu$ has two parts. We find sufficient arithmetic conditions on $p, \lambda, \mu$ for the existence of a nonzero homomorphism $\Delta(\lambda)…

We deal with classes of prime ideals whose associated graded ring is isomorphic to the Rees algebra of the conormal module in order to describe the divisor class group of the Rees algebra and to examine the normality of the conormal module.

Given a parametrization of a rational plane algebraic curve C, some explicit adjoint pencils on C are described in terms of determinants. Moreover, some generators of the Rees algebra associated to this parametrization are presented. The…

Many classical ring-theoretic results state that an ideal that is maximal with respect to satisfying a special property must be prime. We present a "Prime Ideal Principle" that gives a uniform method of proving such facts, generalizing the…

We characterize contractible curves on proper normal algebraic surfaces in terms of complementary Weil divisors. Using this we generalize the classical criteria of Castelnuovo and Artin. As application we derive a finiteness result on…

Let $\MS_g$ be the moduli space of stable holomorphic vector bundles of rank 2 and fixed determinant of odd degree over a smooth complex projective curve of genus $g$. This paper proves various properties of the rational cohomology ring…

We present algorithms to factorize weighted homogeneous elements in the first polynomial Weyl algebra and $q$-Weyl algebra, which are both viewed as a $\mathbb{Z}$-graded rings. We show, that factorization of homogeneous polynomials can be…

Delsarte showed that for any projective linear code over a finite field of characteristic p with two nonzero Hamming weights w1 < w2 there exist positive integers u and s such that w1 = (p^s)u and w2 = (p^s)(u+1). Moreover, he showed that…

The results of [1,2] on linear homogeneous two-weight codes over finite Frobenius rings are exended in two ways: It is shown that certain non-projective two-weight codes give rise to strongly regular graphs in the way described in [1,2].…

For the coinvariant rings of finite Coxeter groups of types other than H$_4$, we show that a homogeneous element of degree one is a strong Lefschetz element if and only if it is not fixed by any reflections. We also give the necessary and…

In this paper, we investigate primeness of groupoid graded rings. We provide a set of necessary and sufficient conditions for primeness of a nearly-epsilon strongly groupoid graded ring. Furthermore, we apply our main result to get a…