Polynomial rings over pseudovaluation rings.
Polynomial rings with coefficients in an intersection of fibred products. (Anneaux de polynômes à coefficients dans une intersection de produits fibrés.)
Polynomials generated by the Fibonacci sequence.
Polynomials with high multiplicity
Polynomials with minimal value set over Galois rings.
Polynomials with values which are powers of integers
Let be a polynomial with integral coefficients. Shapiro showed that if the values of at infinitely many blocks of consecutive integers are of the form , where is a polynomial with integral coefficients, then for some polynomial . In this paper, we show that if the values of at finitely many blocks of consecutive integers, each greater than a provided bound, are of the form where is an integer greater than 1, then for some polynomial .
Polyserial modules over valuation domains
P-orderings and polynomial functions on arbitrary subsets of Dedekind rings.
Porjective Modules over Polynomial 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.
Positive polynomials and hyperdeterminants
Let F be a homogeneous real polynomial of even degree in any number of variables. We consider the problem of giving explicit conditions on the coefficients so that F is positive definite or positive semi-definite. In this note we produce a necessary condition for positivity, and a sufficient condition for non-negativity, in terms of positivity or semi-positivity of a one-variable characteristic polynomial of F. Also, we revisit the known sufficient condition in terms of Hankel matrices.
Positive polynomials and polynomial inequalities.
Positivity in coefficient-free rank two cluster algebras.
Positivity of the -system cluster algebra.
Post algebras in 3-rings.
Potenzreihenerweiterung und formale Fasern in lokalen Ringen mit Approximationseigenschaft.
Power Series over Coherent Rings.
Power Series Solutions of Algebraic Differential Equations.
Powersum formula for differential resolvents.
Powersum formula for polynomials whose distinct roots are differentially independent over constants.