English

Notes on additively divisible commutative semirings

Commutative Algebra 2014-01-14 v1

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.

Keywords

Cite

@article{arxiv.1401.2836,
  title  = {Notes on additively divisible commutative semirings},
  author = {Tomáš Kepka and Miroslav Korbelář},
  journal= {arXiv preprint arXiv:1401.2836},
  year   = {2014}
}

Comments

8 pages

R2 v1 2026-06-22T02:44:01.827Z