### Description

We will investigate polynomials and polynomial functions over finite rings, such as the integers modulo a power of a prime. Concerning polynomial functions, we are interested in the structure of the group of polynomial permutations of a finite ring, and in the structure of projective limits of such groups. These we will investigate with respect to embedding wreath-products of cyclic groups, and eventually, maybe, arbitrary finite p-groups.

Concerning the polynomials themselves, we investigate non-unique factorization into irreducibles. According to previous research

the sets of lengths show a behaviour different from that in rings

that are better known, such as orders in number fields or rings of integer-valued polynomials. Many traditional methods of the theory of non-unique factorization (transfer homomorphisms, conductors) are not applicable to polynomials over finite rings, so we will need to forge new methods.

Concerning the polynomials themselves, we investigate non-unique factorization into irreducibles. According to previous research

the sets of lengths show a behaviour different from that in rings

that are better known, such as orders in number fields or rings of integer-valued polynomials. Many traditional methods of the theory of non-unique factorization (transfer homomorphisms, conductors) are not applicable to polynomials over finite rings, so we will need to forge new methods.

Status | Active |
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Effective start/end date | 1/03/15 → 29/02/20 |