# Principal local Artinian ring is a quotient of discrete valuation ring.

I have seen here the following statement:

Let $R$ be a principal local Artinian ring. Clearly the quotient of a discrete valuation ring is such a ring; conversely it is not difficult to show that every principal local artinian ring is a quotient of a discrete valuation ring.

But there was no proof there. Does anyone know the proof or a reference? (At least for the case of perfect residue field of characteristic $p$ which I am interested in especially.)

• – user26857 Apr 9 '16 at 18:42
• Dear @user26857, thank you for your answer. That's exactly what I want!! – MiRi_NaE Apr 21 '16 at 1:48