Why I am being able to delete a root ownedfile?

Ok, there is this file "a" that has rwx permissions for everyone, so anyone can erase it.

I use cp to create "a2". a2 is created with has similar permissions, excepted that, for some reason, it does not allow members of other groups to write it. Then I use chown to make it to belong to root.

Yet, when I return to my normal user, I can erase it. How is that possible? And how I can avoid it?

Thanks for the help.