Abstract
We study ideal-simple commutative semirings and summarize the results giving their classification, in particular when they are finitely generated. In the principal case of (para)semifields, we then consider their minimal number of generators and show that it grows linearly with the depth of an associated rooted forest.
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Acknowledgements
We thank Miroslav Korbelář and Jiří Šíma for helpful discussions and suggestions, and the anonymous referee for a number of very useful corrections and suggestions (in particular, for proposing Theorem 6.3 and its proof).
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V. K. was supported by Czech Science Foundation GAČR, Grant 21-00420M, and Charles University Research Centre program UNCE/SCI/022.
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Kala, V., Šíma, L. On minimal semiring generating sets of finitely generated commutative parasemifields. Algebra Univers. 85, 24 (2024). https://doi.org/10.1007/s00012-024-00853-9
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DOI: https://doi.org/10.1007/s00012-024-00853-9