Sequences between d-sequences and sequences of linear type

Hamid Kulosman

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 1, page 1-9
  • ISSN: 0010-2628

Abstract

top
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 generate 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.

How to cite

top

Kulosman, Hamid. "Sequences between d-sequences and sequences of linear type." Commentationes Mathematicae Universitatis Carolinae 50.1 (2009): 1-9. <http://eudml.org/doc/32476>.

@article{Kulosman2009,
abstract = {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 generate 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.},
author = {Kulosman, Hamid},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ideal of linear type; c-sequence; d-sequence; sequence of linear type; ideal of linear type; -sequence; -sequence; sequence of linear type},
language = {eng},
number = {1},
pages = {1-9},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Sequences between d-sequences and sequences of linear type},
url = {http://eudml.org/doc/32476},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Kulosman, Hamid
TI - Sequences between d-sequences and sequences of linear type
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 1
SP - 1
EP - 9
AB - 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 generate 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.
LA - eng
KW - ideal of linear type; c-sequence; d-sequence; sequence of linear type; ideal of linear type; -sequence; -sequence; sequence of linear type
UR - http://eudml.org/doc/32476
ER -

References

top
  1. Costa D., 10.1016/0021-8693(85)90211-X, J. Algebra 94 (1985), 256--263. (1985) Zbl0595.13001MR0789548DOI10.1016/0021-8693(85)90211-X
  2. Fiorentini M., 10.1016/0021-8693(71)90068-8, J. Algebra 18 (1971), 384--389. (1971) Zbl0224.13011MR0277517DOI10.1016/0021-8693(71)90068-8
  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. Zbl0499.13002MR0686942
  4. Huneke C., 10.1016/0021-8693(80)90179-9, J. Algebra 62 (1980), 268--275. (1980) Zbl0439.13001MR0563225DOI10.1016/0021-8693(80)90179-9
  5. Huneke C., 10.1080/00927878108822586, Comm. Algebra 9 (1981), 339--366. (1981) Zbl0454.13003MR0605026DOI10.1080/00927878108822586
  6. Huneke C., 10.1016/0001-8708(82)90045-7, Adv. in Math. 46 (1982), 249--279. (1982) Zbl0505.13004MR0683201DOI10.1016/0001-8708(82)90045-7
  7. Kühl M., 10.1007/BF01239944, Manuscripta Math. 37 (1982), 49--60. (1982) MR0649563DOI10.1007/BF01239944
  8. Valla G., 10.1007/BF01303330, Manuscripta Math. 30 (1980), 239--255. (1980) Zbl0471.13002MR0557107DOI10.1007/BF01303330

NotesEmbed ?

top

You must be logged in to post comments.