Having index on the root and wp on another directory

Hi,
I installed wordpress on my site in a directory called /wordpress/
and want to leave it as it is
but I would like my browser to point directry to wordpress, typing my site and not my site/wordpress
that is, https://www.audiomontaggi.net instead of https://www.audiomontaggi.net/wordpress
i have wp 2.0.4. And, unfortunately, I find no .htaccess file on the wp directory (/wordpress/)
I just did as follows:
created a new index.php file, a blank page
with these lines:

<?php
/* Short and sweet */
define('WP_USE_THEMES', true);
require('./wordpress/wp-blog-header.php');
?>

well, I just modified my home page template to fit my needs, that is, to great registered people by name
(welcome Username…if you are not Username…logout)
and for anonymous users, I just built a condition if…else, which shows google adsense banners to anonymous users and invites them to register.
The problem is, that if you type the whole path, https://www.audiomontaggi.net/wordpress, it works correctly. The visitor is automatically recognized.
If you type just the home page, the index points correctly to wordpress
but the user is not recognized; well it asks to login, the function used is wp_loginout(), and when you click on login link, at least me (admin) just leads me to admin panel
…my site is italian only
so, please, if you have any idea of how and what to do, please help me
otherwise another way to make my site point to wordpress without typing /wordpress
via .htaccess, that I am not able to use it
thanks in advance