Models, Modules and Abelian Groups (eBook)

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

Frontmatter 1
Contents 7
Anthony Leonard Southern Corner 1934–2006 11
Groups of units of orders in Q-algebras 19
Basic subgroups and freeness, a counterexample 73
An extension of Butler’s theorem on endomorphism rings 85
Locally free abelian groups of finite rank 93
Decompositions of global crq-groups 109
Endomorphisms and automorphisms of squares of abelian groups 131
Classification of a class of finite rank Butler groups 145
Quotient divisible and almost completely decomposable groups 157
Pure subgroups of completely decomposable groups – an algorithmic approach 179
Strong subgroup chains and the Baer–Specker group 197
On direct decompositions of Butler B(2)-groups 209
Diagonal equivalence of matrices 229
Root bases of polynomials over integral domains 245
A solution to a problem on lattice isomorphic Abelian groups 259
A note on Axiom 3 and its dual for abelian groups 267
Units of modular p-mixed abelian group algebras 277
Pure covers in abelian p-groups 287
Partially decomposable primary Abelian groups and the generalized core class property 299
The additive group of a finite local ring in which each ideal can be n-generated 311
A Jacobson radical isomorphism theorem for torsion-free modules 319
Anti-isomorphisms and the failure of duality 325
Automorphism groups of models of first order theories 335
The classification problem for finite rank Butler groups 339
L-groups 349
Co-local subgroups of nilpotent groups of class 2 361
Divisible envelopes and cotorsion pairs over integral domains 369
The first Brauer–Thrall conjecture 379
A version of the Baer splitting problem for noetherian rings 385
Characterizations and constructions of h-local domains 395
Variations on Whitehead’s problem and the structure of Ext 417
The lattice of torsionfree precover classes 425
Non-singular rings of injective dimension 1 431
On classes defining a homological dimension 441
Truncated path algebras are homologically transparent 455
Representations of the category of serial modules of finite Goldie dimension 473
Commutativity modulo small endomorphisms and endomorphisms of zero algebraic entropy 497