On the order theory for ${\mathcal{C}}^{\infty }$-reduced ${\mathcal{C}}^{\infty }$-Rings and applications

Abstract

In the present work we carry on the study of the order theory for (${\mathcal{C}}^{\infty }-$-reduced) ${\mathcal{C}}^{\infty }-$-rings initiated in \cite{rings1} (see also \cite{BM2}). In particular, we apply some results of the order theory of ${\mathcal{C}}^{\infty }-$-fields (e.g., every such field is real closed) to present another approach to the order theory of general ${\mathcal{C}}^{\infty }-$-rings: "smooth real spectra" (see \cite{separation}). This suggests that a model-theoretic investigation of the class of ${\mathcal{C}}^{\infty }-$-fields could be interesting and also useful to provide the first steps towards the development of the "Real Algebraic Geometry" of ${\mathcal{C}}^{\infty }-$-rings.

32 pages

References in corpus (2)

• A Universal Algebraic Survey of ${\mathcal{C}}^{\infty }-$Rings
• Separation Theorems in Smooth Commutative Algebra and Applications

Cited by in corpus (1)

• Separation Theorems in Smooth Commutative Algebra and Applications