Herve, a serial number (or more appropriately it's ORM name: stock.production.lot) in OpenERP/Odoo can both represent single or a lot of article.  By default there is no validation on whether the serial number.  I used the product_serial module to further fine tune the validation and grouping (splitting, etc) of the serial number.

To use a serial number in general you just need to create the serial number, and then use it in when you create a stock.move.  A serial number is tied to a product.