Given a right ideal I in ring R, the idealizer of R is largest subring which becomes two-sided ideal. In this paper we consider idealizers second Weyl algebra A2, differential operators on k[x,y] (in characteristic 0). Specifically, let f be polynomial x and y defines an irreducible curve whose singularities are all cusps. We show that fA2 A2 always left noetherian, extending work McCaffrey.

Technical elastomers are usually quasi-incompressible. For simulations they are, therefore, often modeled as ideal incompressible or a linear relation between the hydrostatic pressure and (volumetric) dilation is assumed, i.e., constant bulk modulus. However, for strongly compressed structural components, like sealings damper elements, nonlinear material model compression behavior required in o...

We investigate Sharifan and Moradi’s closed neighborhood ideal of a finite simple graph, which is square-free monomial in polynomial ring over field. explicitly describe the minimal irreducible decompositions these ideals. also characterize trees whose ideals are Cohen–Macaulay; particular, this property for characteristic independent.

A square complex matrix A is eventually nonnegative if there exists a positive integer k0 such that for all k ≥ k0, A ≥ 0; A is strongly eventually nonnegative if it is eventually nonnegative and has an irreducible nonnegative power. It is proved that a collection of elementary Jordan blocks is a Frobenius Jordan multiset with cyclic index r if and only if it is the multiset of elementary Jorda...

We investigate the symmetry component of the center variety of polynomial differential systems, corresponding to systems with an axis of symmetry in the real plane. We give a general algorithm to find this component, compute its dimension and show that it is irreducible. We show that our methods provide a simple way to compute the radical of the ideal generated by the focus quantities and, ther...

In this paper, we present a modular strategy which describes key properties of the absolute primary decomposition of an equidimensional polynomial ideal defined by polynomials with rational coefficients. The algorithm we design is based on the classical technique of elimination of variables and colon ideals and uses a tricky choice of prime integers to work with. Thanks to this technique, we ca...

In the last twenty years several methods for computing primary decompositions of ideals in multivariate polynomial rings over fields (Seidenberg (1974), Lazard (1985), Kredel (1987), Eisenbud et al. (1992)), the integers (Seidenberg, 1978), factorially closed principal ideal domains (Ayoub (1982), Gianni et al. (1988)) and more general rings (Seidenberg, 1984) have been proposed. A related prob...

The diagonal in a product of projective spaces is cut out by the ideal of 2×2-minors of a matrix of unknowns. The multigraded Hilbert scheme which classifies its degenerations has a unique Borel-fixed ideal. This Hilbert scheme is generally reducible, and its main component is a compactification of PGL(d)/PGL(d). For n = 2 we recover the manifold of complete collineations. For projective lines ...

In the paper the definition and main properties of a 2D-digraph, namely a directed graph with two kinds of arcs, are introduced. Under the assumption of strong connectedness, the analysis of its paths and cycles is performed, basing on an integer matrix whose rows represent the compositions of all circuits, and on the corresponding row-module. Natural constraints on the composition of the paths...