I only have experience with keyboards so I'm sorry if this sounds like a stupid question. There's a keyboard out there I'm looking at eventually buying. However, it doesn't have any preset rythyms like most portable/arranger type keyboards have. So is there something out there that has strictly rythyms I can use to accompany me while I'm playing? Like a drum module?

Yes.

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I think all the arranger keyboards can do what you want. They have two buttons for styles. If you just press "start," drums is what you get. When you press the other button, often labaled "accompaniment," that's when the piano bass and guitar come in.

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There are also a great number of separate units you can buy that can play drums while you play piano. Here is a link to one of them:
http://www.samedaymusic.com/browse--Boss-Drum-Machines--2963

There are a great many kinds of devices like this. You will need expert advice to make sure you are buying exactly what you need. I am not an expert in this area.

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This particular keyboard doesn't have any type of accompaniment on it, just piano and organ. So a separate unit would be required. I take it the technical term for what i'm looking for is a "drum machine"? I've seen them but I never knew what a drum machine was. I thought maybe it was something you use with a digital drum set.

There are many available , new and used..
Roland and Boss make a great line[many to choose ]..Yamaha makes great units also..
Alesis SR16 sells new for under $150 now and has been a great unit for many years...

Boss DR-770.
You can program each of the 16 Pads to play 2 variations and 2 Fill ins just like an arranger.