On the dispersions of the polynomial maps over finite fields.
On the divisibility of polynomials with integer coefficients.
On the divisibility properties of families of filtered F-crystals.
On the dual of a finitely generated multiplication module II
On the dual of an ideal and ideal Transforms
On the embedding dimension of an affine variety.
On the endomorphism ring and Cohen-Macaulayness of local cohomology defined by a pair of ideals
Let , , be ideals of a Noetherian local ring . Let and be finitely generated -modules. We give a generalized version of the Duality Theorem for Cohen-Macaulay rings using local cohomology defined by a pair of ideals. We study the behavior of the endomorphism rings of and , where is the smallest integer such that the local cohomology with respect to a pair of ideals is nonzero and is the Matlis dual functor. We show that if is a -dimensional complete Cohen-Macaulay ring and ...
On the equations of Rees algebras.
On the equivalence of algebraic and geometric local cohomology
In this paper, we will present several necessary and sufficient conditions on a commutative ring such that the algebraic and geometric local cohomologies are equivalent.
On the family relation for artinian rings
On the field of definition of superspecial polarized abelian varieties and type numbers
On the Finite Generation of Symbolic Blow-Ups.
On the formal first cocycle equation for iteration groups of type II
Let x be an indeterminate over ℂ. We investigate solutions αn : ℂ → ℂ, n ≥ 0, of the first cocycle equation in ℂ [[x]], the ring of formal power series over ℂ, where (F(s,x))s ∈ ℂ is an iteration group of type II, i.e. it is a solution of the translation equation of the form F(s,x) ≡ x + ck(s)xk mod xk+1, where k ≥ 2 and ck ≠ 0 is necessarily an additive function. It is easy to prove that the coefficient functions αn(s) of are polynomials in ck(s).It is possible to replace...
On the formal inverse of polynomial endomorphisms
On the Forster-Eisenbud-Evans Conjectures.
On the free character of the first Koszul homology module.
Let (A,M,K) denote a local noetherian ring A with maximal ideal M and residue field K. Let I be an ideal of A and E the Koszul complex generated over A by a system of generators of I.The condition: H1(E) is a free A/I-module, appears in several important results of Commutative Algebra. For instance:- (Gulliksen [3, Proposition 1.4.9]): The ideal I is generated by a regular sequence if and only if I has finite projective dimension and H1(E) is a free A/I-module.- (André [2]): Assume that A is a complete...
On the free resolutions of local cohomology modules with respect to an ideal generated by a U.S. D-sequence
On the Galois structure of the square root of the codifferent
Let be a finite abelian extension of , with the ring of algebraic integers of . We investigate the Galois structure of the unique fractional -ideal which (if it exists) is unimodular with respect to the trace form of .
On the generalization of the Fibonacci-coefficient polynomials.
On the generalized Davenport constant and the Noether number
Known results on the generalized Davenport constant relating zero-sum sequences over a finite abelian group are extended for the generalized Noether number relating rings of polynomial invariants of an arbitrary finite group. An improved general upper degree bound for polynomial invariants of a non-cyclic finite group that cut out the zero vector is given.