%0 Journal Article
%T K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Roberto, Kaique Matias de Andrade
%A Mariano, Hugo Luiz
%D 2022
%\ 07/01/2022
%V 17
%N 1
%P 1-46
%! K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories
%K quadratic forms
%K special groups
%K K-theory
%K multirings
%K hyperfields
%R 10.52547/cgasa.2021.101755
%X We build on previous work on multirings ([17]) that providesgeneralizations of the available abstract quadratic forms theories (specialgroups and real semigroups) to the context of multirings ([10], [14]). Herewe raise one step in this generalization, introducing the concept of pre-specialhyperfields and expand a fundamental tool in quadratic forms theory to themore general multivalued setting: the K-theory. We introduce and developthe K-theory of hyperbolic hyperfields that generalize simultaneously Milnorâ€™sK-theory ([11]) and Special Groups K-theory, developed by Dickmann-Miraglia ([5]). We develop some properties of this generalized K-theory, thatcan be seen as a free inductive graded ring, a concept introduced in [2] inorder to provide a solution of Marshallâ€™s Signature Conjecture.
%U https://cgasa.sbu.ac.ir/article_101755_c8a4e43e111cf70f030b33574d574259.pdf