Is there some reason why you can not use ls -1 ?

$ ls -1 /other/directory
file1
file2

EDIT:

I notice you've changed the question now - my solution won't work with your new example of ls /other/directory/*.txt. Use something like khachik's solution instead, e.g.

$ (cd /other/directory && ls -1 *.txt)

ls -1 /other/directory/*.txt |xargs basename

• -1 will list one file per line with just the file name (or path)
• Using a wildcard and/or giving ls a full path will output the full, absolute path for each file. basename will strip the path leaving you with just the file name.

1) I'm not sure this shouldn't be on superuser.com

2) ls doesn't print the full path anyway: ls -1 /your/dir

Edit The question has changed. Per Paul's comment below I am updating my answer. You can do it like this:

ls -1 /home/rich/*.txt | sed s/^.*\\/\//

That's a minus 1, not l, although l works too. Explanation: ls -l/-1 writes out the file names with the stuff you don't want. Each line is piped through sed, which here is doing a substitution, as specified by the s/. A substitution takes the form:

s/text/replacement/

We are substituting everything from the beginning of the line ^ upto the last / (/ is a special character so we have to escape it \\/) with nothing - i.e removing it, and thus leaving you with just the filename.

for i in `ls /some/directory` ;do basename $i;done

The expression in `` gets expanded to the files, then each of them is passed to basename. Caveat: Does not work with files containing white spaces!

Try;

ls /other/directory/*.txt | xargs -n 1 basename