can 2 arduino reading from the same eeprom?

simple question, can 2 arduino's reading from the same eeprom?
if yes how?

Same internal EEPROM - no.
Same external EEPROM - maybe.

sorry i forgot to mention it, yes externall eeprom

Yes, and quite easily, conceptually.
Both arduinos just need some external hardware to allow sharing of the control lines. Not hard to do.
Are you planning on an Serial EEPROM or a parallel access EEPROM?
If parallel, I submitted a design for sharing address/data/control a while ago that Leo72 (I think) implemented.
If serial that would be even simpler as there are only like 4 lines to deal with.

serial

I2C? Using the wire library?

Say you had a part like this

You'd tie the 3 address lines hi/lo as needed for the address you select (can be all low).
tie write protect low so either part can write to it.

You might be able to get away with using
Wire.begin(), do your reading/writing,
then
Wire.end(), and set the SDA/SCL pins as inputs, and let the other arduino know the device is available.

Then the other side can do the same sequence.

If that doesn't work, then you can add a tristate buffer, like 74xx244, after each arduino's SDC/SCL driver, and tristate the control lines when not talking to the device so the other side can access the part.
http://focus.ti.com/docs/prod/folders/print/sn74hc244a.html

Or maybe pull write protect high, and have each part pull it low as part of the write sequence.

Connect the 2 arduino's grounds, but only connect power to the EEPROM & buffer from one +5V source.