Algebraic properties of indigenous semirings
Hussein Behzadipour (Sharif University of Technology)
Henk Koppelaar (TU Delft - Interactive Intelligence)
Peyman Nasehpour (The New York Academy of Sciences)
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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 Sierpiński 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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