Conjectures on additively divisible commutative semirings

Year, pages: 2016, 1059 - 1064

We present a series of open questions about finitely generated commutative semirings with divisible additive semigroup. In this context we show that a finitely generated additively divisible commutative semiring is idempotent, provided that it is torsion. In the particular case of a one-generated additively divisible semiring without unit, such a semiring must contain an ideal of idempotent elements.

Kepka, T., Korbelář, M. 2016. Conjectures on additively divisible commutative semirings. In Mathematica Slovaca, vol. 66, no.5, pp. 1059-1064. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0203

Kepka, T., Korbelář, M. (2016). Conjectures on additively divisible commutative semirings. Mathematica Slovaca, 66(5), 1059-1064. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0203