Models, Modules and Abelian Groups: In Memory of A. L. S. Corner

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Models, Modules and Abelian Groups

In Memory of A. L. S. Corner

Edited by: and

Language: English

Published/Copyright: 2008

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About this book

This is a memorial volume dedicated to A. L. S. Corner, previously Professor in Oxford, who published important results on algebra, especially on the connections of modules with endomorphism algebras. The volume contains refereed contributions which are related to the work of Corner. It contains also an unpublished extended paper of Corner himself.

A memorial volume with important contributions related to algebra.

Author / Editor information

Rüdiger Göbel, University Duisburg-Essen, Germany; Brendan Goldsmith, Dublin Institute of Technology, Ireland.

Topics

Mathematics Algebra and Number Theory

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Frontmatter
I

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Contents
VII

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Anthony Leonard Southern Corner 1934–2006
1
B. Goldsmith

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Groups of units of orders in Q-algebras
9
A. L. S. Corner

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Basic subgroups and freeness, a counterexample
63
A. Blass and S. Shelah

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An extension of Butler’s theorem on endomorphism rings
75
R. Göbel and J. Matz

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Locally free abelian groups of finite rank
83
D. M. Arnold

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Decompositions of global crq-groups
99
A. Mader, L.G. Nongxa and M.A. Ould-Beddi

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Endomorphisms and automorphisms of squares of abelian groups
121
G. Cälugäreanu and P. Schultz

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Classification of a class of finite rank Butler groups
135
E. Blagoveshchenskaya

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Quotient divisible and almost completely decomposable groups
147
A. A. Fomin

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Pure subgroups of completely decomposable groups – an algorithmic approach
169
D. Herden and L. Strüngmann

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Strong subgroup chains and the Baer–Specker group
187
O. Kolman

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On direct decompositions of Butler B(2)-groups
199
C. Vivo and C. Metelli

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Diagonal equivalence of matrices
219
A. Mader and O. Mutzbauer

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Root bases of polynomials over integral domains
235
E. F. Cornelius and P. Schultz

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A solution to a problem on lattice isomorphic Abelian groups
249
G. Cälugäreanu and K.M. Rangaswamy

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A note on Axiom 3 and its dual for abelian groups
257
P. Hill and W. Ullery

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Units of modular p-mixed abelian group algebras
267
W. May

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Pure covers in abelian p-groups
277
L. Fuchs and T. Okuyama

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Partially decomposable primary Abelian groups and the generalized core class property
289
P.W. Keef

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The additive group of a finite local ring in which each ideal can be n-generated
301
K. R. Mclean

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A Jacobson radical isomorphism theorem for torsion-free modules
309
M. Flagg

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Anti-isomorphisms and the failure of duality
315
A. L. S. Corner, B. Goldsmith and S.L. Wallutis

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Automorphism groups of models of first order theories
325
V. V. Bludov, M. Giraudet, A.M.W. Glass and G. Sabbagh

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The classification problem for finite rank Butler groups
329
S. Thomas

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L-groups
339
T. G. Faticoni

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Co-local subgroups of nilpotent groups of class 2
351
J. Buckner and M. Dugas

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Divisible envelopes and cotorsion pairs over integral domains
359
L. Salce

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The first Brauer–Thrall conjecture
369
C. M. Ringel

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A version of the Baer splitting problem for noetherian rings
375
C. Greither, D. Herbera and J. Trlifaj

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Characterizations and constructions of h-local domains
385
B. Olberding

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Variations on Whitehead’s problem and the structure of Ext
407
C. U. Jensen

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The lattice of torsionfree precover classes
415
L. Bican

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Non-singular rings of injective dimension 1
421
U. Albrecht

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On classes defining a homological dimension
431
F. Mantese and A. Tonolo

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Truncated path algebras are homologically transparent
445
A. Dugas, B. Huisgen-Zimmermann and J. Learned

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Representations of the category of serial modules of finite Goldie dimension
463
A. Facchini and P. Příhoda

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Commutativity modulo small endomorphisms and endomorphisms of zero algebraic entropy
487
L. Salce and P. Zanardo

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Publishing information

Pages and Images/Illustrations in book

eBook published on:

December 10, 2008

eBook ISBN:

9783110203035

Hardcover published on:

November 17, 2008

Hardcover ISBN:

9783110194371

Pages and Images/Illustrations in book

Front matter:

9

Main content:

497

Other:

1 frontispiece

https://doi.org/10.1515/9783110203035

eBook ISBN: 9783110203035

Hardcover ISBN: 9783110194371

Keywords for this book

Algebra; Commutative Ring; Module; Ring; Indecomposable Module

Audience(s) for this book

Lecturers, Graduate Students of Mathematics; Academic Libraries

Safety & product resources

Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com

Models, Modules and Abelian Groups

Overview

About this book

Author / Editor information

Topics

Table of contents

Frontmatter

Contents

Anthony Leonard Southern Corner 1934–2006

Groups of units of orders in Q-algebras

Basic subgroups and freeness, a counterexample

An extension of Butler’s theorem on endomorphism rings

Locally free abelian groups of finite rank

Decompositions of global crq-groups

Endomorphisms and automorphisms of squares of abelian groups

Classification of a class of finite rank Butler groups

Quotient divisible and almost completely decomposable groups

Pure subgroups of completely decomposable groups – an algorithmic approach

Strong subgroup chains and the Baer–Specker group

On direct decompositions of Butler B(2)-groups

Diagonal equivalence of matrices

Root bases of polynomials over integral domains

A solution to a problem on lattice isomorphic Abelian groups

A note on Axiom 3 and its dual for abelian groups

Units of modular p-mixed abelian group algebras

Pure covers in abelian p-groups

Partially decomposable primary Abelian groups and the generalized core class property

The additive group of a finite local ring in which each ideal can be n-generated

A Jacobson radical isomorphism theorem for torsion-free modules

Anti-isomorphisms and the failure of duality

Automorphism groups of models of first order theories

The classification problem for finite rank Butler groups

L-groups

Co-local subgroups of nilpotent groups of class 2

Divisible envelopes and cotorsion pairs over integral domains

The first Brauer–Thrall conjecture

A version of the Baer splitting problem for noetherian rings

Characterizations and constructions of h-local domains

Variations on Whitehead’s problem and the structure of Ext

The lattice of torsionfree precover classes

Non-singular rings of injective dimension 1

On classes defining a homological dimension

Truncated path algebras are homologically transparent

Representations of the category of serial modules of finite Goldie dimension

Commutativity modulo small endomorphisms and endomorphisms of zero algebraic entropy

Bibliographic data