Vol. 111, No. 2, 1984

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On asymptotic prime divisors

Louis Jackson Ratliff, Jr.

Vol. 111 (1984), No. 2, 395–413

Several results are proved concerning the set Â(I) = {P Spec R; P is a prime divisor of the integral closure (Ii)a of Ii for all large i}, where I is an ideal in a Noetherian ring R. Among these are: if P is a prime divisor of (Ii)a for some i 1, then P is a prime divisor of (In)a for all n i; a characterization of Cohen-Macaulay rings and of altitude two local UFDs in terms of Â(I); and, some results on the relationship of Â(I) to Â(IS) with S a flat R-algebra and to Â((I + z)∕z) with z a minimal prime ideal in R.

Mathematical Subject Classification 2000
Primary: 13A15
Secondary: 13E05, 13B20
Received: 11 June 1982
Revised: 10 August 1982
Published: 1 April 1984
Louis Jackson Ratliff, Jr.