Displaying similar documents to “Decomposition of a semiring into division semirings”

Finite Product of Semiring of Sets

Roland Coghetto (2015)

Formalized Mathematics

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We formalize that the image of a semiring of sets [17] by an injective function is a semiring of sets.We offer a non-trivial example of a semiring of sets in a topological space [21]. Finally, we show that the finite product of a semiring of sets is also a semiring of sets [21] and that the finite product of a classical semiring of sets [8] is a classical semiring of sets. In this case, we use here the notation from the book of Aliprantis and Border [1].

Nil-extensions of completely simple semirings

Sunil K. Maity, Rituparna Ghosh (2013)

Discussiones Mathematicae - General Algebra and Applications

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A semiring S is said to be a quasi completely regular semiring if for any a ∈ S there exists a positive integer n such that na is completely regular. The present paper is devoted to the study of completely Archimedean semirings. We show that a semiring S is a completely Archimedean semiring if and only if it is a nil-extension of a completely simple semiring. This result extends the crucial structure theorem of completely Archimedean semigroup.

Semirings embedded in a completely regular semiring

M. K. Sen, S. K. Maity (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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Recently, we have shown that a semiring S is completely regular if and only if S is a union of skew-rings. In this paper we show that a semiring S satisfying a 2 = n a can be embedded in a completely regular semiring if and only if S is additive separative.