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