Mail Server without domain name

["David Smith " <david_smith_2003@xxxxxxxxxxx>]

Hello List

I want to learn how to set up a complete mail server.

So I started trying to setup the smtp and pop3 services and I found it easy at first.

The real question is:  Can I have a mail server even if I don't have a domain name??

I started trying to retrive mail using a pop3 client installed in my machine and everything ok.

Then I did the same but from a client like eudora or outlook in a computer (pop3) somewhere in internet and I 
used as pop3 server name my IP address and it worked.  

After what I tried to send mail to accounts in other servers and It didn't worked.

I really at last, install IMP  the  Horde IMAP Client as a web interface and also let my users use the SMTP and 
POP3 services..

I've found many tutorials, manual and guides on configuring a mail server on linux and especially in redhat9, 
my distribution, but all of them are based on domain names and I don't have one.

I've tried follow these tutorial "replacing" every domain ocurrence for my IP address but it didn't work.

Is it possible to configure everything nedded without a domain name ?

Thanx in advance

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