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arXiv · 2412.02118

Algebraic properties of Indigenous semirings

Hussein Behzadipour·Henk Koppelaar·Peyman Nasehpour
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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.

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Hussein Behzadipour, Henk Koppelaar, Peyman Nasehpour. 2024-12-03. Algebraic properties of Indigenous semirings. https://doi.org/10.1142/s2811007225500051

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