| dc.creator | Rump, Wolfgang | |
| dc.date | 2010-06-01 | |
| dc.identifier | https://revistas.ufro.cl/ojs/index.php/cubo/article/view/1409 | |
| dc.identifier | 10.4067/S0719-06462010000200007 | |
| 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. | en-US |
| dc.format | application/pdf | |
| dc.language | eng | |
| dc.publisher | Universidad de La Frontera. Temuco, Chile. | en-US |
| dc.relation | https://revistas.ufro.cl/ojs/index.php/cubo/article/view/1409/1262 | |
| dc.source | CUBO, A Mathematical Journal; Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal; 97–121 | en-US |
| dc.source | CUBO, A Mathematical Journal; Vol. 12 Núm. 2 (2010): CUBO, A Mathematical Journal; 97–121 | es-ES |
| dc.source | 0719-0646 | |
| dc.source | 0716-7776 | |
| dc.subject | prime | en-US |
| dc.subject | valuation | en-US |
| dc.subject | product formula | en-US |
| dc.title | The tree of primes in a field | en-US |
| dc.type | info:eu-repo/semantics/article | |
| dc.type | info:eu-repo/semantics/publishedVersion | |
