A procedure to compute prime filtration

Asia Rauf

Open Mathematics (2010)

  • Volume: 8, Issue: 1, page 26-31
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Asia Rauf. "A procedure to compute prime filtration." Open Mathematics 8.1 (2010): 26-31. <http://eudml.org/doc/269014>.

@article{AsiaRauf2010,
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.},
author = {Asia Rauf},
journal = {Open Mathematics},
keywords = {Prime filtrations; Monomial ideal; Stanley decomposition; prime filtrations; monomial ideal},
language = {eng},
number = {1},
pages = {26-31},
title = {A procedure to compute prime filtration},
url = {http://eudml.org/doc/269014},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Asia Rauf
TI - A procedure to compute prime filtration
JO - Open Mathematics
PY - 2010
VL - 8
IS - 1
SP - 26
EP - 31
AB - 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.
LA - eng
KW - Prime filtrations; Monomial ideal; Stanley decomposition; prime filtrations; monomial ideal
UR - http://eudml.org/doc/269014
ER -

References

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  1. [1] Greuel G.-M., Pfister G., A Singular introduction to commutative algebra, 2nd ed., Springer-Verlag, 2007 
  2. [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 Zbl0902.14040
  3. [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 Zbl1107.13017
  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 Zbl1186.13019
  5. [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 Zbl1142.13022
  6. [6] Matsumura H., Commutative ring theory, Cambridge University Press, Cambridge, 1986 
  7. [7] Rauf A., Stanley decompositions, pretty clean filtrations and reductions modulo regular elements, Bull. Math. Soc. Sc. Math. Roumanie, 2007, 50(98), 347–354 Zbl1155.13311
  8. [8] Rauf A., Depth and Stanley depth of multigraded modules, preprint available at http://arxiv.org/abs/0812.2080v2 Zbl1193.13025

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