Algebraic properties of Indigenous semirings
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913790315986944 |
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| author | Behzadipour, Hussein Koppelaar, Henk Nasehpour, Peyman |
| author_facet | Behzadipour, Hussein Koppelaar, Henk Nasehpour, Peyman |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02118 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic properties of Indigenous semirings Behzadipour, Hussein Koppelaar, Henk Nasehpour, Peyman Commutative Algebra Discrete Mathematics Rings and Algebras 16Y60, 13A15, 01A07 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. |
| title | Algebraic properties of Indigenous semirings |
| topic | Commutative Algebra Discrete Mathematics Rings and Algebras 16Y60, 13A15, 01A07 |
| url | https://arxiv.org/abs/2412.02118 |