| Title:
|
Stanley decompositions and polarization (English) |
| Author:
|
Ahmad, Sarfraz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
483-493 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $I$. (English) |
| Keyword:
|
monomial ideals |
| Keyword:
|
partitionable simplicial complexes |
| Keyword:
|
multicomplexes |
| Keyword:
|
Stanley ideals |
| Keyword:
|
polarization |
| MSC:
|
13C14 |
| MSC:
|
13F20 |
| MSC:
|
13F55 |
| MSC:
|
13H10 |
| idZBL:
|
Zbl 1249.13016 |
| idMR:
|
MR2905417 |
| DOI:
|
10.1007/s10587-011-0067-1 |
| . |
| Date available:
|
2011-06-06T10:36:04Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141547 |
| . |
| Reference:
|
[1] Anwar, I.: Janet's algorithm.Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 51(99) (2008), 11-19. Zbl 1164.13010, MR 2396280 |
| Reference:
|
[2] Anwar, I., Popescu, D.: Stanley conjecture in small embedding dimension.J. Algebra 318 (2007), 1027-1031. Zbl 1132.13009, MR 2371984, 10.1016/j.jalgebra.2007.06.005 |
| Reference:
|
[3] Bruns, W., Herzog, J.: Cohen-Macaulay Rings. Rev. edition.Cambridge University Press Cambridge (1998). MR 1251956 |
| Reference:
|
[4] Cimpoeas, M.: Stanley depth of complete intersection monomial ideals.Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 51(99) (2008), 205-211. Zbl 1174.13033, MR 2433498 |
| Reference:
|
[5] Cimpoeas, M.: Stanley depth for monomial ideals in three variables.Preprint (2008), Arxiv:Math.AC/0807.2166. MR 3085722 |
| Reference:
|
[6] Herzog, J., Jahan, A. Soleyman, Yassemi, S.: Stanley decompositions and partitionable simplicial complexes.J. Algebr. Comb. 27 (2008), 113-125. MR 2366164, 10.1007/s10801-007-0076-1 |
| Reference:
|
[7] Herzog, J., Jahan, A. Soleyman, Zheng, X.: Skeletons of monomial ideals.Math. Nachr (to appear). MR 2744136 |
| Reference:
|
[8] Herzog, J., Popescu, D.: Finite filtrations of modules and shellable multicomplexes.Manuscr. Math. 121 (2006), 385-410. Zbl 1107.13017, MR 2267659, 10.1007/s00229-006-0044-4 |
| Reference:
|
[9] Herzog, J., Vladoiu, M., Zheng, X.: How to compute the Stanley depth of a monomial ideal.J. Algebra 322 (2009), 3151-3169. Zbl 1186.13019, MR 2567414, 10.1016/j.jalgebra.2008.01.006 |
| Reference:
|
[10] Jahan, A. Soleyman: Prime filtrations of monomial ideals and polarizations.J. Algebra 312 (2007), 1011-1032. MR 2333198, 10.1016/j.jalgebra.2006.11.002 |
| Reference:
|
[11] Nasir, S.: Stanley decomposition and localization.Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 51(99) (2008), 151-158. MR 2423489 |
| Reference:
|
[12] Popescu, D.: Stanley depth of multigraded modules.J. Algebra 321 (2009), 2782-2797. Zbl 1179.13016, MR 2512626, 10.1016/j.jalgebra.2009.03.009 |
| Reference:
|
[13] Popescu, D., Qureshi, Muhammad I.: Computing the Stanley depth.\ Arxiv:Math. AC/\allowbreak0907.0912. Zbl 1201.13004, MR 2609185 |
| Reference:
|
[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. Zbl 1155.13311, MR 2370321 |
| Reference:
|
[15] Stanley, R. P.: Linear Diophantine equations and local cohomology.Invent. Math. 68 (1982), 175-193. Zbl 0516.10009, MR 0666158, 10.1007/BF01394054 |
| . |
