Some properties of positive derivations on f-rings II

Abstract

Theorem 10(b)(i) in the article "Some properties of positive derivations on f -rings" by Henriksen and Smith asserts that if D is a positive derivation on a reduced f -ring and if x ∈ ker D, then {x} ⊥⊥ ⊆ ker D. A counterexample is provided to show that this assertion is false, and correct proofs are given for some results in the paper by Henriksen and Smith that use Theorem 10(b)(i) in their proofs.