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PreprintCC BY 4.0arXiv

Congruence-simple multiplicatively idempotent semirings and multiplicative divisibility

  • Damian Siejwa
Open at sourcePDFDOICite

Abstract

We resolve two conjectures concerning multiplicatively idempotent semirings. First, we prove that every congruence-simple multiplicatively idempotent semiring is finite, and hence belongs to the finite classification of Kepka, Korbelář and Landsmann. Second, we prove that every finitely generated commutative multiplicatively divisible semiring is multiplicatively idempotent.

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Cite

BibTeXRIS
BibTeX
@misc{siejwa2026congruencesimple,
  title = {{Congruence-simple multiplicatively idempotent semirings and multiplicative divisibility}},
  author = {Damian Siejwa},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29961},
  eprint = {2608.29961},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29961},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Congruence-simple multiplicatively idempotent semirings and multiplicative divisibility
AU  - Damian Siejwa
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29961
UR  - https://arxiv.org/abs/2608.29961
AB  - We resolve two conjectures concerning multiplicatively idempotent semirings. First, we prove that every congruence-simple multiplicatively idempotent semiring is finite, and hence belongs to the finite classification of Kepka, Korbelář and Landsmann. Second, we prove that every finitely generated commutative multiplicatively divisible semiring is multiplicatively idempotent.
ER  -