The chemical identity of an element is basically determined by the number of protons in it's nucleus.
Nucleii can be split but that's not really decay
There are two main modes of radioactive decay the emission of an alpha particle and the emission of a beta particle.
An alpha particle is basically a helium nucleus (2 protons and 2 neutrons) so when a nucleus emits one it drops two protons so moves two places to the left on the periodic table.
eg.
http://www.impcas.ac.cn/usr/wjx/zhonglz/jiangz uo/prc/alpha_decay.gif
Here Americium has changed to Neptunium ( 2 to the left on the periodic table) and it's atomic mass number has dropped 4 (it's lost 2 protons and 2 neutrons)
In beta decay a neutron becomes a proton and emits an electron. Because electrons are so light it's mass stays much the same but it gains a proton for a neutron and so moves one place to the right on the periodic table.
eg.
http://www.impcas.ac.cn/usr/wjx/zhonglz/jiangz uo/prc/tritium_decay.gif
here Tritium ( a form of hydrogen) changes a neutron to a proton and hence becomes Helium 3 (a light form of helium)