Orderings and signatures of higher level on multirings and hyperfields

Autor:	Murray Marshall, Paweł Gładki
Rok vydání:	2012
Předmět:	Subcategory Class (set theory) Pure mathematics Algebra and Number Theory Reflection (mathematics) Geometry and Topology Mathematics
Zdroj:	Journal of K-theory. 10:489-518
ISSN:	1865-5394 1865-2433
DOI:	10.1017/is012004021jkt189
Popis:	Multirings are objects like rings but with multi-valued addition. In the present paper we extend results of E. Becker and others concerning orderings of higher level on fields and rings to orderings of higher level on hyperfields and multirings and, in the process of doing this, we establish higher level analogs of the results previously obtained by the second author. In particular, we introduce a class of multirings called ℓ-real reduced multirings, define a natural reflection A ⇝ Qℓ-red(A) from the category of multirings satisfying to the full subcategory of ℓ-real reduced multirings, and provide an elementary first-order description of these objects. The relationship between ℓ-real reduced hyperfields and the spaces of signatures defined by Mulcahy and Powers is also examined.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ecfc4937c7d806aa835189ecc1271b7f https://doi.org/10.1017/is012004021jkt189 Zobrazit plný text záznamu