K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories
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-specialhyperfield...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Shahid Beheshti University
2022-07-01
|
| Series: | Categories and General Algebraic Structures with Applications |
| Subjects: | |
| Online Access: | https://cgasa.sbu.ac.ir/article_101755_c8a4e43e111cf70f030b33574d574259.pdf |
| _version_ | 1811340359012188160 |
|---|---|
| author | Kaique Roberto Hugo Mariano |
| author_facet | Kaique Roberto Hugo Mariano |
| author_sort | Kaique Roberto |
| collection | DOAJ |
| description | 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 Milnor’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 Marshall’s Signature Conjecture. |
| first_indexed | 2024-04-13T18:40:52Z |
| format | Article |
| id | doaj.art-7a66937af196466aada882968a2dac53 |
| institution | Directory Open Access Journal |
| issn | 2345-5853 2345-5861 |
| language | English |
| last_indexed | 2024-04-13T18:40:52Z |
| publishDate | 2022-07-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj.art-7a66937af196466aada882968a2dac532022-12-22T02:34:44ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612022-07-0117114610.52547/cgasa.2021.101755101755K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms TheoriesKaique Roberto0Hugo Mariano1Instituto de Matemática e Estatística, Universidade de Sao Paulo, Brazil.Instituto de Matemática e Estatística, Universidade de Sao Paulo, Brazil.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 Milnor’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 Marshall’s Signature Conjecture.https://cgasa.sbu.ac.ir/article_101755_c8a4e43e111cf70f030b33574d574259.pdfquadratic formsspecial groupsk-theorymultiringshyperfields |
| spellingShingle | Kaique Roberto Hugo Mariano K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories Categories and General Algebraic Structures with Applications quadratic forms special groups k-theory multirings hyperfields |
| title | K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories |
| title_full | K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories |
| title_fullStr | K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories |
| title_full_unstemmed | K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories |
| title_short | K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories |
| title_sort | k theories and free inductive graded rings in abstract quadratic forms theories |
| topic | quadratic forms special groups k-theory multirings hyperfields |
| url | https://cgasa.sbu.ac.ir/article_101755_c8a4e43e111cf70f030b33574d574259.pdf |
| work_keys_str_mv | AT kaiqueroberto ktheoriesandfreeinductivegradedringsinabstractquadraticformstheories AT hugomariano ktheoriesandfreeinductivegradedringsinabstractquadraticformstheories |