Displaying similar documents to “Semirings without zero divisors.”

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.

σ-ring and σ-algebra of Sets1

Noboru Endou, Kazuhisa Nakasho, Yasunari Shidama (2015)

Formalized Mathematics

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In this article, semiring and semialgebra of sets are formalized so as to construct a measure of a given set in the next step. Although a semiring of sets has already been formalized in [13], that is, strictly speaking, a definition of a quasi semiring of sets suggested in the last few decades [15]. We adopt a classical definition of a semiring of sets here to avoid such a confusion. Ring of sets and algebra of sets have been formalized as non empty preboolean set [23] and field of subsets...