K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 2، دوره 17، شماره 1، مهر 2022، صفحه 1-46 اصل مقاله (527.86 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.52547/cgasa.2021.101755 | ||
| نویسندگان | ||
| Kaique Matias de Andrade Roberto* ؛ Hugo Luiz Mariano | ||
| Instituto de Matemática e Estatística, Universidade de Sao Paulo, Brazil. | ||
| چکیده | ||
| We build on previous work on multirings ([17]) that provides generalizations of the available abstract quadratic forms theories (special groups and real semigroups) to the context of multirings ([10], [14]). 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 ([11]) and Special Groups K-theory, developed by Dickmann- Miraglia ([5]). We develop some properties of this generalized K-theory, that can be seen as a free inductive graded ring, a concept introduced in [2] in order to provide a solution of Marshall’s Signature Conjecture. | ||
| کلیدواژهها | ||
| Quadratic forms؛ special groups؛ K-theory؛ multirings؛ hyperfields | ||
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| مراجع | ||
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