Arithmetic-arboreal residue structures induced by Prufer extensions : An axiomatic approach

TL;DR

This paper develops an axiomatic framework linking Prufer extensions to residue structures, highlighting their arithmetic and arboreal properties, and establishes an adjunction between related functors.

Contribution

It introduces a novel axiomatic approach connecting Prufer extensions with arboreal residue structures and formalizes their relationship via functor adjunctions.

Findings

Established an adjunction between Prufer extensions and superrigid directed commutative regular quasi-semirings.

Provided an axiomatic framework unifying arithmetic and arboreal properties.

Clarified the connection between Prufer extensions and residue structures through categorical relationships.

Abstract

We present an axiomatic framework for the residue structures induced by Prufer extensions with a stress upon the intimate connection between their arithmetic and arboreal theoretic properties. The main result of the paper provides an adjunction relationship between two naturally defined functors relating Prufer extensions and superrigid directed commutative regular quasi-semirings.