What software is available that allows for e-mailing on a local intranet?

My network has four computers connected to it. They all connect to a router to receive internet. One of them receives its connection by wire, two others by wireless and the remaining one does not get internet. I recently connected the computer that does not have internet to the router in preparation for creating an e-mail network. I want each computer to be able to have its own address on the intranet network. I do not want any of the computers to use regular internet e-mail for communication with each other. It is also desirable that the software be freeware and have a file sending feature that would allow transmission of files across the network.