Vol. 67, No. 2, 1976

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The altitude formula and DVR’s

Louis Jackson Ratliff, Jr.

Vol. 67 (1976), No. 2, 509–523
Abstract

The main theorem in this paper characterizes a local domain (R,M) which satisfies the altitude formula in terms of certain DVR’s (discrete valuation rings) in the quotient field F of R. Specifically, R satisfies the altitude formula if and only if every DVRPL (V,N) over R in F (that is, (V,N) is a DVR with quotient field F such that R V , N R = M, and V is integral over a locality over R) is of the first kind (that is, trd (V∕N)(R∕M) = altitude R 1).

Mathematical Subject Classification 2000
Primary: 13G05
Secondary: 13C15, 13D15, 14E25
Milestones
Received: 18 November 1974
Published: 1 December 1976
Authors
Louis Jackson Ratliff, Jr.