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semiring; ideal; simple
Many infinite finitely generated ideal-simple commutative semirings are additively idempotent. It is not clear whether this is true in general. However, to solve the problem, one can restrict oneself only to parasemifields.
[1] El Bashir R., Hurt J., Jančařík A., Kepka T.: Simple commutative semirings. J. Algebra 236 (2001), 277-306. DOI 10.1006/jabr.2000.8483 | MR 1808355 | Zbl 0976.16034
[2] Hebisch U., Weinert H.J.: Halbringe - Algebraische Theorie und Anwendungen in der Informatik. Teubner, Stuttgart, 1993. MR 1311247 | Zbl 0829.16035
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