| Title:
|
Sequences between d-sequences and sequences of linear type (English) |
| Author:
|
Kulosman, Hamid |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
50 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
1-9 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The notion of a d-sequence in Commutative Algebra was introduced by Craig Huneke, while the notion of a sequence of linear type was introduced by Douglas Costa. Both types of sequences gene\-ra\-te ideals of linear type. In this paper we study another type of sequences, that we call c-sequences. They also generate ideals of linear type. We show that c-sequences are in between d-sequences and sequences of linear type and that the initial subsequences of c-sequences are c-sequences. Finally we prove a statement which is useful for computational aspects of the theory of c-sequences. (English) |
| Keyword:
|
ideal of linear type |
| Keyword:
|
c-sequence |
| Keyword:
|
d-sequence |
| Keyword:
|
sequence of linear type |
| MSC:
|
13A15 |
| MSC:
|
13A30 |
| MSC:
|
13B25 |
| MSC:
|
13C13 |
| idZBL:
|
Zbl 1212.13001 |
| idMR:
|
MR2562799 |
| . |
| Date available:
|
2009-08-18T12:22:30Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133410 |
| . |
| Reference:
|
[1] Costa D.: Sequences of linear type.J. Algebra 94 (1985), 256--263. Zbl 0595.13001, MR 0789548, 10.1016/0021-8693(85)90211-X |
| Reference:
|
[2] Fiorentini M.: On relative regular sequences.J. Algebra 18 (1971), 384--389. Zbl 0224.13011, MR 0277517, 10.1016/0021-8693(71)90068-8 |
| Reference:
|
[3] Herzog J., Simis A., Vasconcelos W.: Koszul homology and blowing-up rings.Commutative Algebra (Trento, 1981), Lecture Notes in Pure and Appl. Math. 84, Dekker, New York, 1983, pp. 79--169. Zbl 0499.13002, MR 0686942 |
| Reference:
|
[4] Huneke C.: On the symmetric and Rees algebra of an ideal generated by a d-sequence.J. Algebra 62 (1980), 268--275. Zbl 0439.13001, MR 0563225, 10.1016/0021-8693(80)90179-9 |
| Reference:
|
[5] Huneke C.: Symbolic powers of prime ideals and special graded algebras.Comm. Algebra 9 (1981), 339--366. Zbl 0454.13003, MR 0605026, 10.1080/00927878108822586 |
| Reference:
|
[6] Huneke C.: The theory of d-sequences and powers of ideals.Adv. in Math. 46 (1982), 249--279. Zbl 0505.13004, MR 0683201, 10.1016/0001-8708(82)90045-7 |
| Reference:
|
[7] Kühl M.: On the symmmetric algebra of an ideal.Manuscripta Math. 37 (1982), 49--60. MR 0649563, 10.1007/BF01239944 |
| Reference:
|
[8] Valla G.: On the symmetric and Rees algebras of an ideal.Manuscripta Math. 30 (1980), 239--255. Zbl 0471.13002, MR 0557107, 10.1007/BF01303330 |
| . |
