2020/02/01 by Jean Cerqueira Berni, Berni, Jean Cerqueira, Rodrigo Figueiredo +3
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2002.00268
In the present work we carry on the study of the order theory for\n(\C\∞--reduced) \C\∞--rings initiated in\n citerings1 (see also citeBM2). In particular, we apply some results of\nthe order theory of \C\∞--fields (e.g., every such field is\nreal closed) to present another approach to the order theory of general\n\C\∞--rings: "smooth real spectra" (see citeseparation).\nThis suggests that a model-theoretic investigation of the class of\n\C\∞--fields could be interesting and also useful to provide\nthe first steps towards the development of the "Real Algebraic Geometry" of\n\C\∞--rings.\n