Thumbnail Image
🇬🇧

Complementary decompositions of monomial ideals and involutive bases

Hashemi, Amir
Orth, Matthias
Seiler, Werner M.

Complementary decompositions of monomial ideals - also known as Stanley decompositions - play an important role in many places in commutative algebra. In this article, we discuss and compare several algorithms for their computation. This includes a classical recursive one, an algorithm already proposed by Janet and a construction proposed by Hironaka in his work on idealistic exponents. We relate Janet’s algorithm to the Janet tree of the Janet basis and extend this idea to Janet-like bases to obtain an optimised algorithm. We show that Hironaka’s construction terminates, if and only if the monomial ideal is quasi-stable. Furthermore, we show that in this case the algorithm of Janet determines the same decomposition more efficiently. Finally, we briefly discuss how these results can be used for the computation of primary and irreducible decompositions.

Sponsor
Gefördert im Rahmen des Projekts DEAL
Citation
In: Applicable Algebra in Engineering, Communication and Computing Volume 33 / issue 6 (2022-06-25) , S. 791-821; eissn:1432-0622
Collections
Rights

Creative Commons license

Namensnennung 4.0 International
Except where otherwised noted, this item's license is described as Namensnennung 4.0 International
@article{doi:10.17170/kobra-202301047293,
  author    ={Hashemi, Amir and Orth, Matthias and Seiler, Werner M.},
  title    ={Complementary decompositions of monomial ideals and involutive bases},
  keywords ={510 and Monomiales Ideal and Zerlegung  and Kommutative Algebra},
  copyright  ={http://creativecommons.org/licenses/by/4.0/},
  language ={en},
  journal  ={Applicable Algebra in Engineering, Communication and Computing},
  year   ={2022-06-25}
}