English

Vector spaces over finite commutative rings

Combinatorics 2025-03-28 v2

Abstract

Vector spaces over finite fields and Anzahl formulas of subspaces were studied by Wan (Geometry of Classical Groups over Finite Fields, Science Press, 2002). As a generalization, we study vector spaces and singular linear spaces over commutative rings, and obtain some Anzahl formulas and dimensional formula for subspaces. Moreover, we discuss arcs and caps by using these subspaces.

Keywords

Cite

@article{arxiv.2407.10576,
  title  = {Vector spaces over finite commutative rings},
  author = {Jun Guo and Junli Liu and Qiuli Xu},
  journal= {arXiv preprint arXiv:2407.10576},
  year   = {2025}
}

Comments

19 pages

R2 v1 2026-06-28T17:40:56.560Z