Algebraic properties of Indigenous semirings
Commutative Algebra
2025-04-15 v2 Discrete Mathematics
Rings and Algebras
Abstract
In this paper, we introduce Indigenous semirings and show that they are examples of information algebras. We also attribute a graph to them and discuss their diameters, girths, and clique numbers. On the other hand, we prove that the Zariski topology of any Indigenous semiring is the Sierpi\'{n}ski space. Next, we investigate their algebraic properties (including ideal theory). In the last section, we characterize units and idempotent elements of formal power series over Indigenous semirings.
Keywords
Cite
@article{arxiv.2412.02118,
title = {Algebraic properties of Indigenous semirings},
author = {Hussein Behzadipour and Henk Koppelaar and Peyman Nasehpour},
journal= {arXiv preprint arXiv:2412.02118},
year = {2025}
}
Comments
Minor revision. Some examples and explanations added to the paper