The Krull intersection theorem. II

Daniel D. Anderson, Jacob R. Matijevic and Warren Douglas Nichols

Vol. 66 (1976), No. 1, 15–22

DOI: 10.2140/pjm.1976.66.15

Abstract

Let R be a commutative ring, I an ideal in R and A an R-module. We always have 0 ⊆{a ∈ A|(1 − i)a = 0∃i ∈ I}⊆ I ⋂ _n=1^∞IⁿA ⊆⋂ _n=1^∞IⁿA. In this paper we investigate conditions under which certain of these containments may or may not be replaced by equality.

Mathematical Subject Classification 2000

Primary: 13G05

Secondary: 13C05

Milestones

Received: 28 January 1976

Published: 1 September 1976