A procedure to compute prime filtration

• Autorzy: Asia Rauf
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Prime filtrations; Monomial ideal; Stanley decomposition

Kategorie tematyczne

• 13C15: Dimension theory, depth, related rings (catenary, etc.)
• 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
• 13P10: Gr\"obner bases; other bases for ideals and modules (e.g., Janet and border bases)
• 13F20: Polynomial rings and ideals; rings of integer-valued polynomials

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 1
• Strony: 26-31

Daty

wydano

2010-02-01

online

2010-02-02

Twórcy

autor

Asia Rauf

• GC University

Bibliografia

• [1] Greuel G.-M., Pfister G., A Singular introduction to commutative algebra, 2nd ed., Springer-Verlag, 2007
• [2] 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
• [3] Herzog J., Popescu D., Finite filtrations of modules and shellable multicomplexes, Manuscripta Math., 2006, 121(3), 385–410 http://dx.doi.org/10.1007/s00229-006-0044-4
• [4] Herzog J., Vladoiu M., Zheng X., How to compute the Stanley depth of a monomial ideal, J. Alg., 2009, 322(9), 3151–3169 http://dx.doi.org/10.1016/j.jalgebra.2008.01.006
• [5] Jahan A.S., Prime filtrations of monomial ideals and polarizations, J. Alg., 2007, 312(2), 1011–1032 http://dx.doi.org/10.1016/j.jalgebra.2006.11.002
• [6] Matsumura H., Commutative ring theory, Cambridge University Press, Cambridge, 1986
• [7] Rauf A., Stanley decompositions, pretty clean filtrations and reductions modulo regular elements, Bull. Math. Soc. Sc. Math. Roumanie, 2007, 50(98), 347–354
• [8] Rauf A., Depth and Stanley depth of multigraded modules, preprint available at http://arxiv.org/abs/0812.2080v2

Identyfikatory

DOI

10.2478/s11533-009-0073-9