Make mozilla mail stop checking for mail when closed

I have come to find the preset configuration of mozilla keeping to check 
for mails once the mail client have been opened annoying.

http://www.mozilla.org/start/1.5/faq/mail-news.html

Has this to say:

"The Windows version of Mozilla includes mail notification. It starts 
running in the background when you first open Mozilla Messenger 
(Mail/News), and it continues checking for mail periodically after you 
have closed the Messenger window but with Mozilla still running"

That I know. Now, how do I stop this?
I have looked through the mail.server.default prefs and nothing obvious 
sprung to mind.

Any help would be appreciated.