Mathematics > Commutative Algebra
[Submitted on 3 Dec 2024
(v1)
, last revised 13 Apr 2025 (this version, v2)]
Title: Algebraic properties of Indigenous semirings
Title: Indigenous半环的代数性质
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.
Submission history
From: Peyman Nasehpour [view email][v1] Tue, 3 Dec 2024 03:15:19 UTC (12 KB)
[v2] Sun, 13 Apr 2025 00:22:49 UTC (13 KB)
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