Boolean ideals and their varieties

Samuel Lundqvist

Boolean ideals and their varieties

Commutative Algebra 2019-05-08 v3

Authors: Samuel Lundqvist

Abstract

We consider ideals in the ring $\mathbb{Z}_2[x_1,\ldots, x_n]$ that contain the polynomials $x_i^2 - x_i$ for $i = 1, \ldots, n$ and give various results related to the one-to-one correspondence between these ideals and the subsets of $\mathbb{Z}_2^n$ . We also study the standard monomials with respect to the lexicographical ordering for these ideals and derive a distribution result.

Keywords

ideal theory monomial ideals monomial ideals and free resolutions

Cite

@article{arxiv.1211.3398,
  title  = {Boolean ideals and their varieties},
  author = {Samuel Lundqvist},
  journal= {arXiv preprint arXiv:1211.3398},
  year   = {2019}
}

Comments

22 pages. New title. The connection between the boolean polynomial and its zero set is more carefully studied than in the earlier versions of the paper. There is also an new section about the connection between lexicographical standard monomials and boolean ideals

Boolean ideals and their varieties

Abstract

Keywords

Cite

Comments

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