Local rings with zero-dimensional formal fibers☆
Review articleOpen access
Abstract:

AbstractWe study Noetherian local rings whose all formal fibers are of dimension zero. Universal catenarity and going-up property of the canonical map to the completion are considered. We present several characterizations of these rings, including a characterization of Weierstrass preparation type. A characterization of local rings with going up property by a strong form of Lichtenbaum–Hartshorne Theorem is obtained. As an application, we give an upper bound for dimension of formal fibers of a large class of algebras over these rings.

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