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It is often useful to approach the singularity of a noetherian commutative local domain S from a regulär local subring P over which S is finite äs a module and residually trivial (that is, the induced extension of residue fields is trivial). Such subrings exist in a variety of situations: in commutative algebra they are given by Cohen's structure theory for complete local rings; in analytic geometry they are in place by definition; in algebraic geometry they are sometimes produced by Noether normalization.

Factorial extensions of regular local rings and invariants of finite groups.