I'm trying to lay tile in my kitchen, but I have Linoleum there. I tried to rip it uup but it's not working

There seems to be some clay like tiles under that? My house was builtin 1956 did they use to put someything down on the concrete before they put the Linoleum ? If so can I just tile over that? I know not to tile on Linoleum but what if there is a layer of something else that's hard?