FWF - Poly-Alg - Integer-valued polynomials on algebras

Project: Research project

Project Details

Description

We investigate two kinds of rings of polynomials mapping elements of an algebra to elements of the same algebra.
Both generalize the classical concept of integer-valued polynomials.
An example of the first, commutative, kind of ring is the ring of
polynomials with rational coefficients mapping each n by n integer matrix to an integer matrix. An example of the second, non-commutative, kind of ring is the ring of polynomials with coefficients in the algebra of n by n rational matrices, mapping every n by n integer matrix to an integer matrix.
As with the classical integer-valued polynomials, the main questions concern integral-closure, the Pruefer property, separation of points, polynomial density and non-unique factorization. Both kinds of integer-valued polynomials on algebras require innovative combinations of techniques from commutative ring theory and non-commutative ring
theory for their study. Also, they are useful for constructing rings with certain specified properties (for instance, with respect to factorization).
StatusActive
Effective start/end date1/05/1830/04/22