Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Siejwa, Damian
Institution: Warsaw University of Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204972016