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
Polynomials with minimal value set over Galois rings.
Positive characteristic analogs of closed polynomials
The notion of a closed polynomial over a field of zero characteristic was introduced by Nowicki and Nagata. In this paper we discuss possible ways to define an analog of this notion over fields of positive characteristic. We are mostly interested in conditions of maximality of the algebra generated by a polynomial in a respective family of rings. We also present a modification of the condition of integral closure and discuss a condition involving partial derivatives.
Post algebras in 3-rings.
Presentation depth and the Lipman-Sathaye Jacobian theorem.
Primitive elements in rings of holomorphic functions.
Primitives des fonctions élémentaires
Product formulas for resultants and Chow forms.