On Complement and Supplement Ideals of Nearrings

Yashaswini H L; Vinay Madhusudanan; Kavitha Koppula; Kedukodi Babushri Srinivas; Kuncham Syam Prasad

On Complement and Supplement Ideals of Nearrings

Rings and Algebras 2026-07-09 v1 Combinatorics

Authors: Yashaswini H L , Vinay Madhusudanan , Kavitha Koppula , Kedukodi Babushri Srinivas , Kuncham Syam Prasad

Abstract

In this article we study complement ideals, and the dual concept of supplement ideals, in nearrings, both of which are generalizations of the concept of complement in a bounded modular lattice. We prove fundamental properties of complements and supplements in arbitrary nearrings. We then establish Galois connections between the ideal lattices of a nearring and of its matrix nearrings, yielding one-to-one correspondences between their respective complement and supplement ideals. We also define graphs associated with complement and supplement ideals of nearrings and study some of their combinatorial properties such as girth and clique number.

Keywords

nearrings complement ideals supplement ideals Galois connections matrix nearrings graphs

Cite

@article{arxiv.2607.08311,
  title  = {On Complement and Supplement Ideals of Nearrings},
  author = {Yashaswini H L and Vinay Madhusudanan and Kavitha Koppula and Kedukodi Babushri Srinivas and Kuncham Syam Prasad},
  journal= {arXiv preprint arXiv:2607.08311},
  year   = {2026}
}