Abstract
Let K be a field, S = K[x 1, … x n ] be a polynomial ring in n variables over K and I ⊂ S be an ideal. We give a procedure to compute a prime filtration of S/I. We proceed as in the classical case by constructing an ascending chain of ideals of S starting from I and ending at S. The procedure of this paper is developed and has been implemented in the computer algebra system Singular.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Greuel G.-M., Pfister G., A Singular introduction to commutative algebra, 2nd ed., Springer-Verlag, 2007
Greuel G.-M., Pfister G., Schönemann H., Singular 2.0. A computer algebra system for polynomial computations, Centre for Computer Algebra, University of Kaiserslautern, 2001, http://www.singular.uni-kl.de
Herzog J., Popescu D., Finite filtrations of modules and shellable multicomplexes, Manuscripta Math., 2006, 121(3), 385–410
Herzog J., Vladoiu M., Zheng X., How to compute the Stanley depth of a monomial ideal, J. Alg., 2009, 322(9), 3151–3169
Jahan A.S., Prime filtrations of monomial ideals and polarizations, J. Alg., 2007, 312(2), 1011–1032
Matsumura H., Commutative ring theory, Cambridge University Press, Cambridge, 1986
Rauf A., Stanley decompositions, pretty clean filtrations and reductions modulo regular elements, Bull. Math. Soc. Sc. Math. Roumanie, 2007, 50(98), 347–354
Rauf A., Depth and Stanley depth of multigraded modules, preprint available at http://arxiv.org/abs/0812.2080v2
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Rauf, A. A procedure to compute prime filtration. centr.eur.j.math. 8, 26–31 (2010). https://doi.org/10.2478/s11533-009-0073-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s11533-009-0073-9