Feebly projectable \(\ell \)-groups
type: Item
instance of: scholarly article
title: Feebly projectable \(\ell \)-groups
zbMATH Open document ID: 1192.06014
author: Michelle L. Knox
author: Warren Wm. McGovern
published in: Algebra Universalis
publication date: 2010-06-16T00:00:00Z
review text: The authors remark that, when preparing the present paper, they were motivated by their previous results on frames. Several notions introduced here for \(\ell\)-groups have their counterparts in the theory of frames. An \(\ell\)-group \(G\) is defined to be feebly projectable if whenever \(a,b\in G^+\) are disjoint, then there is \(x\in G^+\) with \(a\in x^{\perp\perp}\), \(b\in x^\perp\), \(G=x^{\perp\perp}\oplus x^\perp\). Further, \(G\) is said to be flatly projectable if for any pair of disjoint elements \(a\) and \(b\), there is a polar subgroup of \(S\) of \(G\) such that \(a\in S\), \(b\in S^\perp\) and \(G=S\oplus S^\perp\). If every prime subgroup of \(G\) contains a minimal prime subgroup then \(G\) is said to have stranded primes. These three notions serve as a main tool in the investigations performed in the paper. Typical results: Suppose that \(\{ G_i\}_{i\in I}\) is a collection of \(\ell\)-groups and \(G=\prod_{i\in I} G_{i}\); then \(G\) is feebly (flatly) projectable if and only if each \(G_i\) is feebly (flatly) projectable. Suppose \(G\) is flatly projectable, then it is representable. Further, the authors prove some related results for Archimedean \(\ell\)-groups with weak order unit and for commutative semiprime \(f\)-rings.
reviewed by: Ján Jakubík
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 06F25
zbMATH DE Number: 5721489
zbMATH Keywords: \(\ell\)-group
zbMATH Keywords: algebraic frame
zbMATH Keywords: \(f\)-ring
MaRDI profile type: Publication
full work available at URL: s00012-010-0041-z
OpenAlex ID: W1999981475
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DOI: 10.1007/S00012-010-0041-Z
description: scientific article; zbMATH DE number 5721489