Vol. 65, No. 2, 1976

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A theorem on prime divisors of zero and characterizations of unmixed local domains

Louis Jackson Ratliff, Jr.

Vol. 65 (1976), No. 2, 449–470

Two characterizations of when the prime divisors of zero in a complete local ring are all minimal are given. Then a number of results which characterize an unmixed local domain R of altitude two are proved. Among these are when certain over-rings of R are finite R-modules and when R is a subspace of certain Macaulay over-rings. Finally, some characterizations of when an arbitrary local domain is unmixed are given.

Mathematical Subject Classification 2000
Primary: 13H99
Received: 26 November 1975
Published: 1 August 1976
Louis Jackson Ratliff, Jr.