 The proof of Hungerford's theorem employs Cohen's structure theorems for complete local rings.Arguing as in Example 3. above and using the Zariski-Samuel theorem, it is easy to check that Hungerford's theorem is equivalent to the statement that any special principal ring is the quotient of a discrete valuation ring.Every semisimple ring "R" which is not just a product of fields is a noncommutative right and left principal ideal domain.