Finitely Generated Congruences in Semirings and Canonical Positive Models

Abstract

In this paper, we explore semirings in which all congruences are finitely generated. Such semirings are dubbed \textit{Congruence Noetherian}. After developing sufficient background and examples, we focus on the canonical positive models of a real order and show that this obvious choice, though not finitely generated as an $\mathbb{N}$-module, is both Congruence Noetherian and flat over $\mathbb{N}$.

Revised v2