Remove part of the values in a column

#1
Probably this is an easy question for experienced R-users, so hopefully you can help me. In my dataframe, I have the following kind of values in my 'RSID'- and 'ALLELE'-columns:

RSID ALLELE
rs12345. A.
rs3984. C.
rs12398432. G.
etc.

Now I need to remove the . after each rs-number.

I tried this option:
df$RSID[df$RSID == "."] <- " "
df$ALLELE[df$ALLELE == "."] <- " "

But unfortunately it did not work. Do you have suggestions?

Thanks in advance!