English

On some notions of rank for matrices over tracts

Combinatorics 2025-07-02 v2 Rings and Algebras

Abstract

Given a tract FF in the sense of Baker and Bowler and a matrix AA with entries in FF, we define several notions of rank for AA. In this way, we are able to unify and find conceptually satisfying proofs for various results about ranks of matrices that one finds scattered throughout the literature.

Keywords

Cite

@article{arxiv.2202.02356,
  title  = {On some notions of rank for matrices over tracts},
  author = {Matthew Baker and Noah Solomon and Tianyi Zhang},
  journal= {arXiv preprint arXiv:2202.02356},
  year   = {2025}
}

Comments

v2: significant rewriting to address suggestions by a referee, added Noah Solomon as a coauthor