2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/107753Let $^*\mathbb{R}$ be a nonstandard extension of $\mathbb{R}$ and $ρ$ be a positive infinitesimal in $^*\mathbb{R}$. We show how to create a variety of isomorphisms between A. Robinson's field of asymptotic numbers $^ρ\mathbb{R}$ and the Hahn field $\hat{^ρ\mathbb{R}}(t^\mathbb{R})$, where $\hat{^ρ\mathbb{R}}$ is the residue class field of $^ρ\mathbb{R}$. Then, assuming that $^*\mathbb{R}$ is fully saturated we show that $\hat{^ρ\mathbb{R}}$ is isomorphic to $^*\mathbb{R}$ and so $^ρ\mathbb{R}$ contains a copy of $^*\mathbb{R}$. As a consequence (that is important for applications in non-linear theory of generalized functions) we show that every two fields of asymptotic numbers corresponding to different scales are isomorphic.18 pagesCommutative AlgebraLogic03H05, 06A05, 12J10, 12J25, 13A18, 16W60text