On the Structure of Complete Local Rings

Abstract

The concept of a local ring was introduced by Krull [2], who defined it as a Noetherian ringR(we say that a commutative ringRis Noetherian if every ideal inRhas a finite basis and ifRcontains the identity) which has only one maximal idealm. If the powers of m are defined as a system of neighbourhoods of zero, thenRbecomes a topological ring satisfying the first axiom of countability, And the notion was studied recentlybyC. Chevalley and I. S. Cohen. Cohen [1] proved the structure theorem for complete rings besides other properties of local rings.