Lamron ℓ-groups

Papiya Bhattacharjee, Warren Wm McGovern

Research output: Contribution to journalArticle

Abstract

The article introduces a new class of lattice-ordered groups. An ℓ-group G is lamron if Min(G)−1 is a Hausdorff topological space, where Min(G)−1 is the space of all minimal prime subgroups of G endowed with the inverse topology. It will be evident that lamron ℓ-groups are related to ℓ-groups with stranded primes. In particular, it is shown that for a W-object (G,u), if every value of u contains a unique minimal prime subgroup, then G is a lamron ℓ-group; such a W-object will be said to have W-stranded primes. A diverse set of examples will be provided in order to distinguish between the notions of lamron, stranded primes, W-stranded primes, complemented, and weakly complemented ℓ-groups.

Original languageEnglish (US)
Pages (from-to)81-98
Number of pages18
JournalQuaestiones Mathematicae
Volume41
Issue number1
DOIs
StatePublished - Sep 16 2018

Fingerprint

Subgroup
Lattice-ordered Group
Topological space
Topology
Object
Class

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Cite this

Bhattacharjee, P., & McGovern, W. W. (2018). Lamron ℓ-groups. Quaestiones Mathematicae, 41(1), 81-98. https://doi.org/10.2989/16073606.2017.1372529
Bhattacharjee, Papiya ; McGovern, Warren Wm. / Lamron ℓ-groups. In: Quaestiones Mathematicae. 2018 ; Vol. 41, No. 1. pp. 81-98.
@article{aaf23f7de35a4d10a367aea5131d4f6c,
title = "Lamron ℓ-groups",
abstract = "The article introduces a new class of lattice-ordered groups. An ℓ-group G is lamron if Min(G)−1 is a Hausdorff topological space, where Min(G)−1 is the space of all minimal prime subgroups of G endowed with the inverse topology. It will be evident that lamron ℓ-groups are related to ℓ-groups with stranded primes. In particular, it is shown that for a W-object (G,u), if every value of u contains a unique minimal prime subgroup, then G is a lamron ℓ-group; such a W-object will be said to have W-stranded primes. A diverse set of examples will be provided in order to distinguish between the notions of lamron, stranded primes, W-stranded primes, complemented, and weakly complemented ℓ-groups.",
author = "Papiya Bhattacharjee and McGovern, {Warren Wm}",
year = "2018",
month = "9",
day = "16",
doi = "10.2989/16073606.2017.1372529",
language = "English (US)",
volume = "41",
pages = "81--98",
journal = "Quaestiones Mathematicae",
issn = "1607-3606",
publisher = "Taylor and Francis Ltd.",
number = "1",

}

Bhattacharjee, P & McGovern, WW 2018, 'Lamron ℓ-groups', Quaestiones Mathematicae, vol. 41, no. 1, pp. 81-98. https://doi.org/10.2989/16073606.2017.1372529

Lamron ℓ-groups. / Bhattacharjee, Papiya; McGovern, Warren Wm.

In: Quaestiones Mathematicae, Vol. 41, No. 1, 16.09.2018, p. 81-98.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Lamron ℓ-groups

AU - Bhattacharjee, Papiya

AU - McGovern, Warren Wm

PY - 2018/9/16

Y1 - 2018/9/16

N2 - The article introduces a new class of lattice-ordered groups. An ℓ-group G is lamron if Min(G)−1 is a Hausdorff topological space, where Min(G)−1 is the space of all minimal prime subgroups of G endowed with the inverse topology. It will be evident that lamron ℓ-groups are related to ℓ-groups with stranded primes. In particular, it is shown that for a W-object (G,u), if every value of u contains a unique minimal prime subgroup, then G is a lamron ℓ-group; such a W-object will be said to have W-stranded primes. A diverse set of examples will be provided in order to distinguish between the notions of lamron, stranded primes, W-stranded primes, complemented, and weakly complemented ℓ-groups.

AB - The article introduces a new class of lattice-ordered groups. An ℓ-group G is lamron if Min(G)−1 is a Hausdorff topological space, where Min(G)−1 is the space of all minimal prime subgroups of G endowed with the inverse topology. It will be evident that lamron ℓ-groups are related to ℓ-groups with stranded primes. In particular, it is shown that for a W-object (G,u), if every value of u contains a unique minimal prime subgroup, then G is a lamron ℓ-group; such a W-object will be said to have W-stranded primes. A diverse set of examples will be provided in order to distinguish between the notions of lamron, stranded primes, W-stranded primes, complemented, and weakly complemented ℓ-groups.

UR - http://www.scopus.com/inward/record.url?scp=85029526216&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85029526216&partnerID=8YFLogxK

U2 - 10.2989/16073606.2017.1372529

DO - 10.2989/16073606.2017.1372529

M3 - Article

VL - 41

SP - 81

EP - 98

JO - Quaestiones Mathematicae

JF - Quaestiones Mathematicae

SN - 1607-3606

IS - 1

ER -

Bhattacharjee P, McGovern WW. Lamron ℓ-groups. Quaestiones Mathematicae. 2018 Sep 16;41(1):81-98. https://doi.org/10.2989/16073606.2017.1372529