I don't want to have a wi-fi signal in my apartment. I have a wired modem. But, for those tenants with a wireless modem and without a password, it is causing problems. Can I scramble the signal so it is not accessible in my apartment?
If the tenants don't have a password, they should not be able to connect, if you disable the wireless part or if you set up your wireless part to require a password.
If you don't want your router to broadcast its presence, you can disable SSID broadcast. Here is some more information: http://compnetworking.about.com/cs/wirelessproducts/qt/disablessidcast.htm
If you're not using the wireless part of your router you should be able to go to the configuration page and disable it.
The exact steps will depend on the router. Check your manual or search online for your router make and model to download the instructions.