The initial meadows

TL;DR

This paper characterizes the initial algebra of meadows, a special class of rings with an inverse operator, and proves that its word problem is decidable, advancing algebraic theory and computational logic.

Contribution

It identifies the initial algebra of characteristic 0 meadows and establishes the decidability of its word problem, a novel theoretical result.

Findings

Initial algebra of characteristic 0 meadows determined

Decidability of the word problem proven

Advances understanding of algebraic structures with inverse operators

Abstract

A \emph{meadow} is a commutative ring with an inverse operator satisfying $0^{-1}=0$. We determine the initial algebra of the meadows of characteristic 0 and show that its word problem is decidable.