English

Gr\"obner bases of contraction ideals

Commutative Algebra 2010-11-05 v2

Abstract

We investigate Gr\"obner bases of contraction ideals under some monomial homomorphisms. As an application of our theorem, we generalize the result of Aoki--Hibi--Ohsugi--Takemura and Hibi-Ohsugi. Using our results, one can provide many examples of toric ideals that admit square-free or quadratic initial ideals.

Keywords

Cite

@article{arxiv.1010.5768,
  title  = {Gr\"obner bases of contraction ideals},
  author = {Takafumi Shibuta},
  journal= {arXiv preprint arXiv:1010.5768},
  year   = {2010}
}

Comments

19 pages, typos corrected, and some minor revisions, Definition 3.10, Proposition 3.11, Example 4.4, and Example 3.23 added

R2 v1 2026-06-21T16:35:08.464Z