When Min(A)⁻¹ is Hausdorff

Abstract

For a commutative ring with identity, say A, its collection of minimal prime ideals is denoted by Min(A). The hull-kernel topology on Min(A) is a well-studied structure. For example, it is known that the hull-kernel topology on Min(A) has a base of clopen subsets, and classifications of when Min(A) is compact abound. Recently, a program of studying the inverse topology on Min(A) has begun. This article adds to the growing literature. In particular, we characterize when Min(A)⁻¹ is Hausdorff. In the final section, we consider rings of continuous functions and supply examples.

Key Words:

• Hull-Kernel topology
• Inverse topology
• Minimal prime ideal
• Rings of continuous functions

2010 Mathematics Subject Classification:

• Primary 13
• Secondary 54G

Notes

Communicated by S. Bazzoni.