When C(X) is an h-local ring

Abstract

An h-local domain is a domain for which each nonzero prime ideal is contained in a unique maximal ideal and each nonzero element has finite character. In his dissertation, A. Omairi generalizes the notion of an h-local domain to rings with zero-divisors by restricting the definition to regular ideals. In this article, we give a characterization of when C(X) the ring of continuous real-valued functions on a space X is an h-local ring. We are left with more questions than answers.

KEYWORDS:

• C(X)
• commutative ring with identityl
• h-local ring

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 13Fxx
• Secondary: 13Axx
• 54G20

Acknowledgments

We would like to thank the referee for their careful reading of the article and their thoughtful suggestions which vastly improved the paper.