# When is a zero dimensional local ring a chain ring?

A commutative ring with identity is called a chain ring if all its ideals form a chain under inclusion. I want to know is there any proof for the fact that a zero dimensional local ring is a chain ring whenever its maximal ideal is principal?

• This is proved in the paper : Hungerford, Thomas W. On the structure of principal ideal rings. Pacific J. Math. 25 1968 543–547. – Matthieu Romagny Jun 4 '18 at 15:22