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
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.