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Full-Text Articles in Mathematics
On T-Pure And Almost Pure Exact Sequences Of Lca Groups, Peter Loth
On T-Pure And Almost Pure Exact Sequences Of Lca Groups, Peter Loth
Mathematics Faculty Publications
A proper short exact sequence in the category of locally compact abelian groups is said to be t-pure if φ(A) is a topologically pure subgroup of B, that is, if for all positive integers n. We establish conditions under which t-pure exact sequences split and determine those locally compact abelian groups K ⊕ D (where K is compactly generated and D is discrete) which are t-pure injective or t-pure projective. Calling the extension (*) almost pure if for all positive integers n, we obtain a complete description of the almost pure injectives and almost pure projectives in the category of …
Compact Topologically Torsion Elements Of Topological Abelian Groups, Peter Loth
Compact Topologically Torsion Elements Of Topological Abelian Groups, Peter Loth
Mathematics Faculty Publications
In this note, we prove that in a Hausdorff topological abelian group, the closed subgroup generated by all compact elements is equal to teh closed subgroup generated by all compact elements which are topologically p-torsion for some prime p. In particular, this yields a new, short solution to a question raised by Armacost [A]. Using Pontrjagin duality, we obtain new descriptions of the identity component of a locally compact abelian group.
Splitting In Locally Compact Abelian Groups, Peter Loth
Splitting In Locally Compact Abelian Groups, Peter Loth
Mathematics Faculty Publications
No abstract provided.
The Duals Of Warfield Groups, Peter Loth
The Duals Of Warfield Groups, Peter Loth
Mathematics Faculty Publications
A Warfield group is a direct summand of a simply presented abelian group. In this paper, we describe the Pontrjagin dual groups of Warfield groups, both for the p-local and the general case. A variety of characterizations of these dual groups is obtained. In addition, numerical invariants are given that distinguish between two such groups which are not topologically isomorphic.
The Persistence Of Universal Formulae In Free Algebras, Anthony M. Gaglione, Dennis Spellman
The Persistence Of Universal Formulae In Free Algebras, Anthony M. Gaglione, Dennis Spellman
Mathematics Faculty Publications
Gilbert Baumslag, B.H. Neumann, Hanna Neumann, and Peter M. Neumann successfully exploited their concept of discrimination to obtain generating groups of product varieties via the wreath product construction. We have discovered this same underlying concept in a somewhat different context. Specifically, let V be a non-trivial variety of algebras. For each cardinal α let Fα(V) be a V-free algebra of rank α. Then for a fixed cardinal r one has the equivalence of the following two statements ...