English

Generalized Binomial Edge Ideals

Commutative Algebra 2014-06-18 v1

Abstract

This paper studies a class of binomial ideals associated to graphs with finite vertex sets. They generalize the binomial edge ideals, and they arise in the study of conditional independence ideals. A Gr\"obner basis can be computed by studying paths in the graph. Since these Gr\"obner bases are square-free, generalized binomial edge ideals are radical. To find the primary decomposition a combinatorial problem involving the connected components of subgraphs has to be solved. The irreducible components of the solution variety are all rational.

Keywords

Cite

@article{arxiv.1210.7960,
  title  = {Generalized Binomial Edge Ideals},
  author = {Johannes Rauh},
  journal= {arXiv preprint arXiv:1210.7960},
  year   = {2014}
}

Comments

6 pages. arXiv admin note: substantial text overlap with arXiv:1110.1338

R2 v1 2026-06-21T22:29:57.055Z