# Structure theorems for modules over 'good' rings

Structure theorem for finitely-generated modules over PID is well-known fact. But is there similar theorems for modules(maybe finitely-generated) over noetherian or artin or some other 'good' rings? I particularly want to know it in case $M$ is graded or have finite length.

• The structure of finitely generated modules over finite dimensional algebras over fields can be very complicated, see mathoverflow.net/questions/5895/… – egreg Mar 14 '15 at 21:47