The tree of primes in a field

dc.creator	Rump,Wolfgang
dc.date	2010-01-01
dc.date.accessioned	2017-03-07T16:36:23Z
dc.date.available	2017-03-07T16:36:23Z
dc.identifier	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462010000200007
dc.identifier.uri	http://repositorioslatinoamericanos.uchile.cl/handle/2250/404491
dc.description	The product formula of algebraic number theory connects finite and infinite primes in a stringent way, a fact, while not hard to be checked, that has never ceased to be tantalizing. We propose a new concept of prime for any field and investigate some of its properties. There are algebraic primes, corresponding to valuations, such that every prime contains a largest algebraic one. For a number field, this algebraic part is zero just for the infinite primes. It is shown that the primes of any field form a tree with a kind of self-similar structure, and there is a binary operation on the primes, unexplored even for the rationals. Every prime defines a topology on the field, and each compact prime gives rise to a unique Haar measure, playing an essential part in the product formula.
dc.format	text/html
dc.language	en
dc.publisher	Universidad de La Frontera. Departamento de Matemática y Estadística
dc.publisher	Universidade Federal de Pernambuco. Departamento de Matemática
dc.source	Cubo (Temuco) v.12 n.2 2010
dc.subject	prime
dc.subject	valuation
dc.subject	product formula
dc.title	The tree of primes in a field
dc.type	Artículos de revistas