(Might be off topic) Bash question

[Daniel Marques]

Hi.  Couldn't find another bash newsgroup.  Hope someone can help out.
Anyway...

Is there a way for bash (on machine x) to tell if it is being run as
result of an rsh issued on machine y?
Is there a way to determine the machine/domain name of machine y?

I would like to rsh into a remote machine x, and have bash automatically
set DISPLAY to machine y.

Thanks.

Dan