Primary powers of a prime ideal

L. Robbiano and Giuseppe Valla

Vol. 63 (1976), No. 2, 491–498

DOI: 10.2140/pjm.1976.63.491

Abstract

In this paper we show that the powers of a prime ideal p are primary iff the direct summands of the graded ring associated with p are torsion-free. We prove some consequences of this fact especially in connection with geometric situations.

Mathematical Subject Classification 2000

Primary: 14M10

Secondary: 13A15

Milestones

Received: 22 July 1975

Revised: 9 December 1975

Published: 1 April 1976