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ℵ k -free separable groups with prescribed endomorphism ring

Daniel Herden, Héctor Gabriel Salazar Pedroza (2015)

Fundamenta Mathematicae

We will consider unital rings A with free additive group, and want to construct (in ZFC) for each natural number k a family of ℵ k -free A-modules G which are separable as abelian groups with special decompositions. Recall that an A-module G is ℵ k -free if every subset of size < ℵ k is contained in a free submodule (we will refine this in Definition 3.2); and it is separable as an abelian group if any finite subset of G is contained in a free direct summand of G. Despite the fact that such a module G is...

(1,4)-groups with homocyclic regulator quotient of exponent p³

David M. Arnold, Adolf Mader, Otto Mutzbauer, Ebru Solak (2015)

Colloquium Mathematicae

The class of almost completely decomposable groups with a critical typeset of type (1,4) and a homocyclic regulator quotient of exponent p³ is shown to be of bounded representation type. There are precisely four near-isomorphism classes of indecomposables, all of rank 6.

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