A generalization of von Neumann regularity

Autor:	Claude Sureson
Rok vydání:	2005
Předmět:	Discrete mathematics Pure mathematics Mathematics::Commutative Algebra Logic Generalization Valuation (logic) symbols.namesake Boolean space Completeness (order theory) symbols Von Neumann regular ring Special case Axiom Mathematics Von Neumann architecture
Zdroj:	Annals of Pure and Applied Logic. 135:210-242
ISSN:	0168-0072
DOI:	10.1016/j.apal.2005.02.002
Popis:	We propose two theories, one generalizing the notion of regularity, the other symmetric to it. Under two additional axioms (as for the Carson–Lipshitz–Saracino theorems) one obtains model completeness of both theories. Models of these theories can be viewed as rings of sections (over a boolean space) of sheaves whose stalks are valuation rings. Regular rings correspond to the special case where all stalks are trivial valuation rings, that is fields.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::efbb726e0cb747851335d3323b6dc82b https://doi.org/10.1016/j.apal.2005.02.002 Zobrazit plný text záznamu Full Text from ScienceDirect