A note on finitely generated ideal-simple commutative semirings
Vítězslav Kala, Tomáš Kepka (2008)
Commentationes Mathematicae Universitatis Carolinae
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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.