Flexible involutive meadows

TL;DR

This paper introduces flexible involutive meadows, a new algebraic structure generalizing involutive meadows by defining a notion of inverse for neutrices, with potential applications beyond nonstandard analysis.

Contribution

It defines and characterizes flexible involutive meadows, extending the concept of involutive meadows to a broader algebraic framework inspired by neutrices.

Findings

Axiomatic characterization of flexible involutive meadows

Generalization of involutive meadows beyond nonstandard analysis

Potential applications in algebra and analysis

Abstract

We investigate a notion of inverse for neutrices inspired by Van den Berg and Koudjeti's decomposition of a neutrix as the product of a real number and an idempotent neutrix. We end up with an algebraic structure that can be characterized axiomatically and generalizes involutive meadows. The latter are algebraic structures where the inverse for multiplication is a total operation. As it turns out, the structures satisfying the axioms of flexible involutive meadows are of interest beyond nonstandard analysis.