Finitely Generated Congruences in Semirings and Canonical Positive Models

2025/11/16 by Sen, Snehinh
#13F20 #16Y60 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2511.12815

Abstract

In this paper, we inspect a relatively unexplored notion of finite generation in semirings, namely semirings in which all congruences are finitely generated. Such semirings are dubbed 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 ℕ-module, is both Congruence Noetherian and flat over ℕ.

Citations

• Facets of module theory over semirings
• On k-Noetherian and k-Artinian Semirings
• Witt vectors, semirings, and total positivity

Related

• Finite generation of a canonical ring
• Semigroups for which every right congruence of finite index is finitely generated
• Simulation vs. Equivalence
• The commutative algebra of congruence ideals and applications to number theory
• k-Congruences on semirings