A characterization of analytically unramified semi-local rings and applications

Louis Jackson Ratliff, Jr.

Vol. 27 (1968), No. 1, 127–143

DOI: 10.2140/pjm.1968.27.127

Abstract

It is proved that a semi-local ring R is analytically unramified if and only if R is a subspace of a ring which is isomorphic to a finite direct sum of semi-local Dedekind domains. Applying this, it is proved that a local domain R is analytically irreducible if and only if R is a subspace of a local Dedekind domain, and this is true if and only if R is a subspace of every local domain which dominates R and which satisfies the altitude formula relative to R. A final application proves that an analytically unramified local domain is unmixed if and only if it satisfies the altitude formula.

Mathematical Subject Classification

Primary: 13.50

Milestones

Received: 7 September 1967

Published: 1 October 1968