Pseudoprime L-Ideals in a Class of F-Rings

In a commutative f-ring, an l-ideal I is called pseudoprime if ab = 0 implies a ∈ I or b ∈ I, and is called square dominated if for every a ∈ I, |a| ≤ x ² for some x ∈ A such that x ² ∈ I. Several characterizations of pseudoprime l-ideals are given in the class of commutative semiprime f-rings in which minimal prime l-ideals are square dominated. It is shown that the hypothesis imposed on the f-rings, that minimal prime l-ideals are square dominated, cannot be omitted or generalized.