On quotient rings of pointfree function rings
Abstract
Let L be a completely regular frame. Associated with each I ∈ βL are two ideals, MI and OI, of the ring of real-valued continuous functions on a frame L. In this paper, we describe the intersection of all essential maximal ideals of an f-ring as the ideal MA , with A equal to the join of all nowhere dense sublocales of βL. We show that every prime ideal of is essential if and only if A is a perfect sublocale. A ring is an EI N -ring if and only if L is an EF-frame. We show that is an EI N-ring if and only if the sublocale A (regarding A as a frame in itself ) is an EF-frame if and only if is an EI N-ring.
Fields of Study & Subjects
Rings
Modules
and Algebras
Commutative Algebra and Its Applications
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Quaestiones Mathematicae
- Publisher
- National Inquiry Services Center (NISC)
- Volume
- 49
- Issue
- 4
- Pages
- 525–547
- Publication date
- 8 January 2026
- Language
- EN