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Notes on additively divisible commutative semirings

2014/01/13 by Tomáš Kepka, Kepka, Tomáš, Miroslav Korbelář +1
Mathematics · Computer Science · #Rings, Modules, and Algebras #Advanced Algebra and Logic #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1401.2836

Abstract

Commutative semirings with divisible additive semigroup are studied. We show that an additively divisible commutative semiring is idempotent, provided that it is finitely generated and torsion. In case that a one-generated additively divisible semiring posseses no unit, it must contain an ideal of idempotent elements. We also present a series of open questions about finitely generated commutative semirings and their equivalent versions.

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