Generalized p-Adic Constructions

Abstract

In this paper “abstract lifting algorithms” for polynomial equations over a commutative ring with identity element are developed. They lift solutions modulo some ideal I to solutions modulo another ideal $J \subset I$ (e.g. $J = I^T $). These algorithms are obtained by applying Newton’s method to the polynomial equations and include for example the Hensel-type polynomial factorization algorithms as special cases.