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On the Structure of Complete Local Rings

1950; Cambridge University Press; Volume: 1; Linguagem: Inglês

10.1017/s0027763000022844

2152-6842

Masayoshi Nagata,

Commutative Algebra and Its Applications

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