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Infinite Abelian groups
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The article was published on 1970-01-01 and is currently open access. It has received 2613 citations till now. The article focuses on the topics: Elementary abelian group & Rank of an abelian group.read more
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Journal ArticleDOI
Differentially Trivial and Rigid Rings of Finite Rank
TL;DR: In this article, the authors study the rings of finite rank which have only trivial derivations (respectively endomorphisms) and characterizations of these rings are given. But the main results are characterizations only of finite-rank rings.
Journal ArticleDOI
Completely decomposable direct summands of torsion-free abelian groups of finite rank
Adolf Mader,Phill Schultz +1 more
TL;DR: In this paper, the authors consider a finite rank torsion-free abelian group and show that there exist direct decompositions where the group is completely decomposable and has no rank 1 direct summand.
Prescribing Endomorphism Algebras of ℵ n -free Modules
TL;DR: In this article, the authors consider almost-free abelian groups and verify the test problems for them by careful choice of particular elements of their endomorphisms rings, and construct a first time more systematically and uniformly ℵn-free R-modules M with n an arbitrary, but fixed natural number, over a domain R with EndR M = R.
Journal ArticleDOI
Classification and direct decompositions of some butler groups of countable rank
TL;DR: In this paper, an extension of results concerning decompositions of particular almost completely decomposable groups of finite rank studied by Mader and the first author in 1-2 to groups of infinite rank was presented.
Book ChapterDOI
Bowen’s Entropy for Endomorphisms of Totally Bounded Abelian Groups
TL;DR: In this paper, it was shown that the complete theorem does not hold for topological metrizable groups, and the authors used the structure theorems for abelian groups, the properties of the Bohr topology and Pontryagin duality to prove it.