For finitely generated modules N ( M over a Noetherian ring R, we study the following properties about primary decomposition: (1) The Compatibility property, which says that if Ass(M/N) = {P1, P2, . . . , Ps} and Qi is a Pi-primary component of N ( M for each i = 1, 2, . . . , s, then N = Q1 ∩Q2 ∩ · · · ∩Qs; (2) For a given subset X = {P1, P2, . . . , Pr} ⊆ Ass(M/N), X is an open subset of Ass(...

We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and the idea of Shimoyama–Yokoyama resp. Eisenbud– Hunecke–Vasconcelos to extract primary ideals from pseudo–primary ideals. A parallelized version of the algor...

In this paper we describe the method which applied to successfully compute primary decomposition of a certain ideal coming from applications in combinatorial algebra and algebraic statistics regarding conditional independence statements with hidden variables. While our is based on algorithm for by Gianni, Trager Zacharias, were not able decompose using standard form that algorithm, nor any othe...