m-Quasinormal f-rings

✍ Scribed by Chawne Monique Kimber

• Book ID: 104152308
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 232 KB
• Volume: 158
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(00)00061-x

✦ Synopsis

Given a completely regular topological space X , we wish to determine the poset structure of the root system of prime ideals of the ring C(X ) of real-valued continuous functions on X ; and vice versa. Here, we describe three measures on the poset of prime subgroups of a lattice-ordered group which determine the arithmetic of the group. Then we show that C(X ) has the property that the sum of any m minimal prime ideals is a maximal ideal or the entire ring if and only if the subspace m j=1 cl(coz(fj)) ⊂ X is a P-space for every pairwise disjoint family {fj} m j=1 ⊂ C(X ).