Characterizations of Chain conditions on finite matrix subgroups

Abdallah Laradji

doi:10.1080/00927872.2010.495737

Characterizations of Chain conditions on finite matrix subgroups

Abdallah Laradji^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We give several characterizations of Zimmermann's uniform chain condition on matrix subgroups. In particular, we prove that a family of modules satisfies it precisely when the direct sum of their pure injective envelopes splits in their direct product. We also prove that a weaker non-uniform version of this condition is equivalent to Σ-algebraic compactness of reduced products.

Original language	English
Pages (from-to)	3104-3113
Number of pages	10
Journal	Communications in Algebra
Volume	39
Issue number	9
DOIs	https://doi.org/10.1080/00927872.2010.495737
State	Published - 2011

Bibliographical note

Funding Information:
The author gratefully acknowledges the support provided by King Fahd University of Petroleum and Minerals.

Keywords

Finite matrix subgroup
Pure injective
Reduced product

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927872.2010.495737

Cite this

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title = "Characterizations of Chain conditions on finite matrix subgroups",

abstract = "We give several characterizations of Zimmermann's uniform chain condition on matrix subgroups. In particular, we prove that a family of modules satisfies it precisely when the direct sum of their pure injective envelopes splits in their direct product. We also prove that a weaker non-uniform version of this condition is equivalent to Σ-algebraic compactness of reduced products.",

keywords = "Finite matrix subgroup, Pure injective, Reduced product",

author = "Abdallah Laradji",

note = "Funding Information: The author gratefully acknowledges the support provided by King Fahd University of Petroleum and Minerals.",

year = "2011",

doi = "10.1080/00927872.2010.495737",

language = "English",

volume = "39",

pages = "3104--3113",

journal = "Communications in Algebra",

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T1 - Characterizations of Chain conditions on finite matrix subgroups

AU - Laradji, Abdallah

N1 - Funding Information: The author gratefully acknowledges the support provided by King Fahd University of Petroleum and Minerals.

PY - 2011

Y1 - 2011

N2 - We give several characterizations of Zimmermann's uniform chain condition on matrix subgroups. In particular, we prove that a family of modules satisfies it precisely when the direct sum of their pure injective envelopes splits in their direct product. We also prove that a weaker non-uniform version of this condition is equivalent to Σ-algebraic compactness of reduced products.

AB - We give several characterizations of Zimmermann's uniform chain condition on matrix subgroups. In particular, we prove that a family of modules satisfies it precisely when the direct sum of their pure injective envelopes splits in their direct product. We also prove that a weaker non-uniform version of this condition is equivalent to Σ-algebraic compactness of reduced products.

KW - Finite matrix subgroup

KW - Pure injective

KW - Reduced product

UR - https://www.scopus.com/pages/publications/80055058113

U2 - 10.1080/00927872.2010.495737

DO - 10.1080/00927872.2010.495737

M3 - Article

AN - SCOPUS:80055058113

SN - 0092-7872

VL - 39

SP - 3104

EP - 3113

JO - Communications in Algebra

JF - Communications in Algebra

IS - 9

ER -

Characterizations of Chain conditions on finite matrix subgroups

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this