Stanley decompositions and polarization

Sarfraz Ahmad

Czechoslovak Mathematical Journal (2011)

  • Volume: 61, Issue: 2, page 483-493
  • ISSN: 0011-4642

Abstract

top
We define nice partitions of the multicomplex associated with a Stanley ideal. As the main result we show that if the monomial ideal I is a CM Stanley ideal, then I p is a Stanley ideal as well, where I p is the polarization of I .

How to cite

top

Ahmad, Sarfraz. "Stanley decompositions and polarization." Czechoslovak Mathematical Journal 61.2 (2011): 483-493. <http://eudml.org/doc/196887>.

@article{Ahmad2011,
abstract = {We define nice partitions of the multicomplex associated with a Stanley ideal. As the main result we show that if the monomial ideal $I$ is a CM Stanley ideal, then $I^p$ is a Stanley ideal as well, where $I^p$ is the polarization of $I$.},
author = {Ahmad, Sarfraz},
journal = {Czechoslovak Mathematical Journal},
keywords = {monomial ideals; partitionable simplicial complexes; multicomplexes; Stanley ideals; polarization; monomial ideal; partitionable simplicial complexes; multicomplexes; Stanley ideal; polarization},
language = {eng},
number = {2},
pages = {483-493},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Stanley decompositions and polarization},
url = {http://eudml.org/doc/196887},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Ahmad, Sarfraz
TI - Stanley decompositions and polarization
JO - Czechoslovak Mathematical Journal
PY - 2011
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 61
IS - 2
SP - 483
EP - 493
AB - We define nice partitions of the multicomplex associated with a Stanley ideal. As the main result we show that if the monomial ideal $I$ is a CM Stanley ideal, then $I^p$ is a Stanley ideal as well, where $I^p$ is the polarization of $I$.
LA - eng
KW - monomial ideals; partitionable simplicial complexes; multicomplexes; Stanley ideals; polarization; monomial ideal; partitionable simplicial complexes; multicomplexes; Stanley ideal; polarization
UR - http://eudml.org/doc/196887
ER -

References

top
  1. Anwar, I., Janet's algorithm, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 51(99) (2008), 11-19. (2008) Zbl1164.13010MR2396280
  2. Anwar, I., Popescu, D., 10.1016/j.jalgebra.2007.06.005, J. Algebra 318 (2007), 1027-1031. (2007) Zbl1132.13009MR2371984DOI10.1016/j.jalgebra.2007.06.005
  3. Bruns, W., Herzog, J., Cohen-Macaulay Rings. Rev. edition, Cambridge University Press Cambridge (1998). (1998) MR1251956
  4. Cimpoeas, M., Stanley depth of complete intersection monomial ideals, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 51(99) (2008), 205-211. (2008) Zbl1174.13033MR2433498
  5. Cimpoeas, M., Stanley depth for monomial ideals in three variables, Preprint (2008), Arxiv:Math.AC/0807.2166. (2008) MR3085722
  6. Herzog, J., Jahan, A. Soleyman, Yassemi, S., 10.1007/s10801-007-0076-1, J. Algebr. Comb. 27 (2008), 113-125. (2008) MR2366164DOI10.1007/s10801-007-0076-1
  7. Herzog, J., Jahan, A. Soleyman, Zheng, X., Skeletons of monomial ideals, Math. Nachr (to appear). MR2744136
  8. Herzog, J., Popescu, D., 10.1007/s00229-006-0044-4, Manuscr. Math. 121 (2006), 385-410. (2006) Zbl1107.13017MR2267659DOI10.1007/s00229-006-0044-4
  9. Herzog, J., Vladoiu, M., Zheng, X., 10.1016/j.jalgebra.2008.01.006, J. Algebra 322 (2009), 3151-3169. (2009) Zbl1186.13019MR2567414DOI10.1016/j.jalgebra.2008.01.006
  10. Jahan, A. Soleyman, 10.1016/j.jalgebra.2006.11.002, J. Algebra 312 (2007), 1011-1032. (2007) MR2333198DOI10.1016/j.jalgebra.2006.11.002
  11. Nasir, S., Stanley decomposition and localization, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 51(99) (2008), 151-158. (2008) MR2423489
  12. Popescu, D., 10.1016/j.jalgebra.2009.03.009, J. Algebra 321 (2009), 2782-2797. (2009) Zbl1179.13016MR2512626DOI10.1016/j.jalgebra.2009.03.009
  13. Popescu, D., Qureshi, Muhammad I., Computing the Stanley depth, Arxiv:Math. AC/0907.0912. Zbl1201.13004MR2609185
  14. Rauf, A., Stanley decompositions, pretty clean filtrations and reductions modulo regular elements, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 50(98) (2007), 347-354. (2007) Zbl1155.13311MR2370321
  15. Stanley, R. P., 10.1007/BF01394054, Invent. Math. 68 (1982), 175-193. (1982) Zbl0516.10009MR0666158DOI10.1007/BF01394054

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.