The dual notion of prime submodules
In this paper the concept of the second submodule (the dual notion of prime submodule) is introduced.
The effect of quadratic transformations on degree functions.
The effect of rational maps on polynomial maps
We describe the polynomials P ∈ ℂ[x,y] such that . As applications we give new examples of bad field generators and examples of families of polynomials with smooth and irreducible fibers.
The effect on associated prime ideals produced by an extension of the base field.
The Elements of K2 (...s).
The embedding dimension of the formal Moduli space of certain curve singularities.
The equality in Buchsbaum rings
The equations of Rees algebras of ideals with linear presentation.
The equations of space curves on a quadric.
The homogeneous ideals of curves in a double plane have been studied by Chiarli, Greco, Nagel. Completing this work we describe the equations of any curve that is contained in some quadric. As a consequence, we classify the Hartshorne-Rao modules of such curves.
The Euler Characteristic of a Finitely Generated Module of Finite Injective Dimension.
The existence of equivariant pure free resolutions
Let be a polynomial ring in variables and let be a strictly increasing sequence of integers. Boij and Söderberg conjectured the existence of graded -modules of finite length having pure free resolution of type in the sense that for the -th syzygy module of has generators only in degree .This paper provides a construction, in characteristic zero, of modules with this property that are also -equivariant. Moreover, the construction works over rings of the form where is a polynomial...
The explicit reciprocity law and the cohomology of Fontaine-Messing
The F4-algorithm for Euclidean rings
In this short note, we extend Faugére’s F4-algorithm for computing Gröbner bases to polynomial rings with coefficients in an Euclidean ring. Instead of successively reducing single S-polynomials as in Buchberger’s algorithm, the F4-algorithm is based on the simultaneous reduction of several polynomials.
The factoriality of Zariski rings
The factorization of the derivative of Dickson polynomials.
The finite free extension of artinian -algebras with the strong Lefschetz property
The First Isomorphism Theorem and Other Properties of Rings
Different properties of rings and fields are discussed [12], [41] and [17]. We introduce ring homomorphisms, their kernels and images, and prove the First Isomorphism Theorem, namely that for a homomorphism f : R → S we have R/ker(f) ≅ Im(f). Then we define prime and irreducible elements and show that every principal ideal domain is factorial. Finally we show that polynomial rings over fields are Euclidean and hence also factorial
The first term in a minimal pure injective resolution.
The five-variable Volterra system
We give a description of all polynomial constants of the five-variable Volterra derivation, hence of all polynomial first integrals of its corresponding Volterra system of differential equations. The Volterra system plays a significant role in plasma physics and population biology.
The F-method and a branching problem for generalized Verma modules associated to
The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras , and generalized conformal -Verma modules of scalar type. As a result, we classify the -singular vectors for this class of -modules.