Displaying similar documents to “Commutative parasemifields finitely generated as semirings”

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.

Notes on commutative parasemifields

Vítězslav Kala, Tomáš Kepka, Miroslav Korbelář (2009)

Commentationes Mathematicae Universitatis Carolinae

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Parasemifields (i.e., commutative semirings whose multiplicative semigroups are groups) are considered in more detail. We show that if a parasemifield S contains ℚ + as a subparasemifield and is generated by ℚ + ∪ { a } , a ∈ S , as a semiring, then S is (as a semiring) not finitely generated.