Some properties of finite meadows

TL;DR

This paper explores the structure of finite meadows, showing they are composed of finite fields combined via finite products, leading to a unique representation of minimal meadows based on prime fields.

Contribution

It establishes that finite meadows are exactly the finite products of finite fields and provides a unique representation of minimal meadows using prime fields.

Findings

Finite meadows are the closure of finite fields under finite products.

Minimal meadows have a unique representation in terms of prime fields.

The structure of finite meadows can be fully characterized by their relation to finite fields.

Abstract

The aim of this note is to describe the structure of finite meadows. We will show that the class of finite meadows is the closure of the class of finite fields under finite products. As a corollary, we obtain a unique representation of minimal meadows in terms of prime fields.