2024/04/04 by Kaique Matias de Andrade Roberto, Hugo Luiz mariano · 1 voice
Mathematics · #math.KT #math.AC
paper · pdf · doi:10.52547/cgasa.2021.223166.1323
We build on previous work on multirings (\citeroberto2021quadratic) that provides generalizations of the available abstract quadratic forms theories (special groups and real semigroups) to the context of multirings (\citemarshall2006real, \citeribeiro2016functorial). Here we raise one step in this generalization, introducing the concept of pre-special hyperfields and expand a fundamental tool in quadratic forms theory to the more general multivalued setting: the K-theory. We introduce and develop the K-theory of hyperbolic hyperfields that generalize simultaneously Milnor's K-theory (\citemilnor1970algebraick) and Special Groups K-theory, developed by Dickmann-Miraglia (\citedickmann2006algebraic). We develop some properties of this generalized K-theory, that can be seen as a free inductive graded ring, a concept introduced in \citedickmann1998quadratic in order to provide a solution of Marshall's Signature Conjecture.