On the ring of quotients of a noetherian commutative ring with respect to the Dickson topology
On the structure and arithmetic of finitely primary monoids
On the structure of certain normal ideals
On the Transitvity of regular differential Forms.
On valuation spectra
One-fibered ideals in 2-dimensional rational singularities that can be desingularized by blowing up the unique maximal ideal
Let (R;m) be a 2-dimensional rational singularity with algebraically closed residue field and whose associated graded ring is an integrally closed domain. Göhner has shown that for every prime divisor v of R, there exists a unique one-fibered complete m-primary ideal A v in R with unique Rees valuation v and such that any complete m-primary ideal with unique Rees valuation v, is a power of A v. We show that for v ≠ ordR, A v is the inverse transform of a simple complete ideal in an immediate quadratic...
Outer automorphisms of endomorphism algebras
Commutative rings over which no endomorphism algebra has an outer automorphism are studied.
Pathological maximal R-sequences in quasilocal domains
Periodicity of Recurring Sequences in Rings.
Polynômes à valeurs entières ainsi que leurs dérivées
Polynomes a Valeurs entieres sur un anneau de Pseudovaluation.
Polynomes à valeurs entières sur un anneau non analytiquement irréductible.
Polynômes de Barsky
Polynômes et dérivées à valeurs entières
Polynomial cycles in certain local domains
1. Let R be a domain and f ∈ R[X] a polynomial. A k-tuple of distinct elements of R is called a cycle of f if for i=0,1,...,k-2 and . The number k is called the length of the cycle. A tuple is a cycle in R if it is a cycle for some f ∈ R[X]. It has been shown in [1] that if R is the ring of all algebraic integers in a finite extension K of the rationals, then the possible lengths of cycles of R-polynomials are bounded by the number , depending only on the degree N of K. In this note we consider...
Polynomial Cycles in Finitely Generated Domains.
Polynomial Extensions and Excision for K1 .
Polynomial rings over Jacobson-Hilbert rings.
All rings considered are commutative with unit. A ring R is SISI (in Vámos' terminology) if every subdirectly irreducible factor ring R/I is self-injective. SISI rings include Noetherian rings, Morita rings and almost maximal valuation rings ([V1]). In [F3] we raised the question of whether a polynomial ring R[x] over a SISI ring R is again SISI. In this paper we show this is not the case.
Polynomials generated by the Fibonacci sequence.
Polynomials with high multiplicity