Integral domain type representations in sheaves and other topoi

Autor:	John F. Kennison
Rok vydání:	1976
Předmět:	Algebra Ordered ring Mathematics::Category Theory General Mathematics Hausdorff space Sheaf Universal algebra State (functional analysis) Type (model theory) Topos theory Integral domain Mathematics
Zdroj:	Mathematische Zeitschrift. 151:35-56
ISSN:	1432-1823 0025-5874
DOI:	10.1007/bf01174724
Popis:	In this paper we examine when an algebra of some kind can be represented as the algebra of sections of, for example, a sheaf whose stalks satisfy first-order conditions. This extends the work of [11] which was mainly restricted to totally Hausdorff representations. The general purpose of this work is to relate (classical) universal algebra to intuitionistic algebra in the spirit of [-16]. Our best results characterize rings of sections of integral domain objects and represent any f-ring by a sheaf of totally ordered rings. In these cases the results are true for an arbitrary topos defined over sets and not just for a spatial topos. (A spatial topos is a category of sheaves over a fixed base. This paper makes sense even if the word " topos" is consistently read as "spatial topos.") We proceed to state our results in detail for integral domain objects and totally ordered ring objects.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::8825d16c05fd874b07febf020bc671cc https://doi.org/10.1007/bf01174724 Zobrazit plný text záznamu Full text from SpringerLink