An improved Ritt-Wu’s decomposition (of an algebraic set into the union of irreducible varieties) algorithm is given. The algorithm has been used to prove geometric theorems that Wu’s original method addresses. Unlike Wu’s original approach, nondegenerate conditions are given explicitly at the beginning, not generated during the proof process. A program based on this improved version of the alg...

A classical theorem by Ritt states that all the complete decomposition chains of a univariate polynomial satisfying a certain tameness condition have the same length. In this paper we present our conclusions about the generalization of these theorem in the case of finite coefficient fields when the tameness condition is dropped. (Updated April 2008: see note at the beginning of the introduction.)

11 A classical theorem by Ritt states that all the complete decomposition chains of a univariate polynomial satisfying a certain tameness condition have the same length. In this paper we present 13 our conclusions about the generalization of these theorem in the case of finite coefficient fields when the tameness condition is dropped. 15 © 2005 Published by Elsevier Inc.

In [2, Chapter VII (p. 133)], Ritt shows an example of two irreducible differential variety of differential dimension 2 in U whose intersection consists of a single point: the origin. The details below follow Ritt’s exposition using more modern language and notation. The first part is taken from my tutorial paper [3], with some change in notation. That paper provides the basic background needed...

In the last twenty years several methods for computing primary decompositions of ideals in multivariate polynomial rings over fields (Seidenberg (1974), Lazard (1985), Kredel (1987), Eisenbud et al. (1992)), the integers (Seidenberg, 1978), factorially closed principal ideal domains (Ayoub (1982), Gianni et al. (1988)) and more general rings (Seidenberg, 1984) have been proposed. A related prob...