Pojective exterior Koszul homology and decomposititon of the Tor fonctor.
Pólya fields and Pólya numbers
A number field , with ring of integers , is said to be a Pólya field if the -algebra formed by the integer-valued polynomials on admits a regular basis. In a first part, we focus on fields with degree less than six which are Pólya fields. It is known that a field is a Pólya field if certain characteristic ideals are principal. Analogously to the classical embedding problem, we consider the embedding of in a Pólya field. We give a positive answer to this embedding problem by showing that...
Pólya fields, Pólya groups and Pólya extensions: a question of capitulation
A number field , with ring of integers , is said to be a Pólya field when the -algebra formed by the integer-valued polynomials on admits a regular basis. It is known that such fields are characterized by the fact that some characteristic ideals are principal. Analogously to the classical embedding problem in a number field with class number one, when is not a Pólya field, we are interested in the embedding of in a Pólya field. We study here two notions which can be considered as measures...
Polyèdre caractéristique et éclatements combinatoires.
Polynôme d'Hilbert-Samuel des clôtures intégrales des puissances d'un idéal m-primaire
Polynômes à valeurs entières ainsi que leurs dérivées
Polynomes à valeurs entières et propriété de Skolem.
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 algebra of constants of the four variable Lotka-Volterra system
We describe the ring of constants of a specific four variable Lotka-Volterra derivation. We investigate the existence of polynomial constants in the other cases of Lotka-Volterra derivations, also in n variables.
Polynomial algebra of constants of the Lotka-Volterra system
Let k be a field of characteristic zero. We describe the kernel of any quadratic homogeneous derivation d:k[x,y,z] → k[x,y,z] of the form , called the Lotka-Volterra derivation, where A,B,C ∈ k.
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 fibre rings of algebras over noetherian rings.
Polynomial orbits in finite commutative rings
Let be a finite commutative ring with unity. We determine the set of all possible cycle lengths in the ring of polynomials with rational integral coefficients.
Polynomial Ring in Two Variables Over a D.V.R.: A Criterion.
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.