The Conductor of one-dimensional Gorenstein Rings in their blowing-up.
The cones associated to some tranversal polymatroids.
The connection between a conjecture of Carlisle and Kropholler, now a theorem of Benson and Crowley-Boevey, and Grothendieck's Riemannian-Roch and duality theorems.
The constants of the Volterra derivation
The ring of constants of the Volterra derivation is found. Confirming a conjecture of Zielinski, it is always a polynomial ring.
The Construction of a Module of Finite Projective Dimension from a Finitely Generated Module of Finite Injective Dimension.
The construction of orthonormal wavelets using symbolic methods and a matrix analytical approach for wavelets on the interval.
The containment property for large quotient rings.
The covariety of perfect numerical semigroups with fixed Frobenius number
Let be a numerical semigroup. We say that is an isolated gap of if A numerical semigroup without isolated gaps is called a perfect numerical semigroup. Denote by the multiplicity of a numerical semigroup . A covariety is a nonempty family of numerical semigroups that fulfills the following conditions: there exists the minimum of the intersection of two elements of is again an element of , and for all such that We prove that the set is a perfect numerical semigroup with...
The covering of rings by valuation rings
The cubic mapping graph for the ring of Gaussian integers modulo
The article studies the cubic mapping graph of , the ring of Gaussian integers modulo . For each positive integer , the number of fixed points and the in-degree of the elements and in are found. Moreover, complete characterizations in terms of are given in which is semiregular, where is induced by all the zero-divisors of .
The cyclic homology and K-theory of curves.
The deformation relation on the set of Cohen-Macaulay modules on a quotient surface singularity
Let X be a quotient surface singularity, and define as the directed graph of maximal Cohen-Macaulay (MCM) modules with edges corresponding to deformation incidences. We conjecture that the number of connected components of is equal to the order of the divisor class group of X, and when X is a rational double point (RDP), we observe that this follows from a result of A. Ishii. We view this as an enrichment of the McKay correspondence. For a general quotient singularity X, we prove the conjecture...
The degree of rational cuspidal curves.
The differential spectrum of a ring
The dimension of certain catalecticant varieties.
The distributivity property of finite intersections of valuation rings
The distributivity property of valuation rings
The Divisor Class Group of Ordinary and Symbolic Blow-ups.
The divisor of the resultant.
The dual notion of prime submodules
In this paper the concept of the second submodule (the dual notion of prime submodule) is introduced.