Some algebraic characterizations of \(F\)-frames
type: Item
instance of: scholarly article
title: Some algebraic characterizations of \(F\)-frames
zbMATH Open document ID: 1225.06007
author: Themba Dube
published in: Algebra Universalis
publication date: 2010-08-13T00:00:00Z
review text: The paper provides a number of equivalent conditions for a completely regular frame to be an \(F\)-frame. In particular, it is shown that a completely regular frame \(L\) is an \(F\)-frame iff the ring \(\mathcal R L\) of continuous real-valued functions on \(L\) is a Bézout ring (Proposition 3.2). It is also shown that \(\mathcal R L\) is almost weak Baer iff \(L\) is a strongly zero-dimensional \(F\)-frame (Proposition 4.9).
reviewed by: Guram Bezhanishvili
Mathematics Subject Classification ID: 06D22
Mathematics Subject Classification ID: 54G05
zbMATH DE Number: 5770089
zbMATH Keywords: rings of continuous functions on a frame
zbMATH Keywords: \(F\)-frame
zbMATH Keywords: strongly zero-dimensional frame
zbMATH Keywords: almost weak Baer ring
zbMATH Keywords: completely regular frame
zbMATH Keywords: Bézout ring
MaRDI profile type: Publication
full work available at URL: s00012-010-0054-7
OpenAlex ID: W2056704974
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DOI: 10.1007/S00012-010-0054-7
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description: scientific article; zbMATH DE number 5770089