On generalized Redei functions.
On mulitplication and factorization of polynomials, II. Irreducibility discussion.
On multiplication and factorization of polynomials, I. Lexicographic orderings and extreme aggregates of terms.
On orthogonal decomposition of homogeneous polynomials
On polynomial mappings into spheres
On the Anderson-Badawi conjecture
Let be a commutative ring with an identity different from zero and be a positive integer. Anderson and Badawi, in their paper on -absorbing ideals, define a proper ideal of a commutative ring to be an -absorbing ideal of , if whenever for , then there are of the ’s whose product is in and conjecture that for any ideal of an arbitrary ring , where . In the present paper, we use content formula techniques to prove that their conjecture is true, if one of the following conditions...
On the construction of explicit solutions to the matrix equation .
On the formal inverse of polynomial endomorphisms
On the generalization of the Fibonacci-coefficient polynomials.
On the irreducibility of pure difference binomials.
On the reduction of Kronecker's modular systems whose elements are functions of two and three variables.
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 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 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.