Document Type

Article

Publication Date

11-2006

Abstract

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 locally compact abelian groups.

Comments

This research was supported by a University Research/Creativity Grant (URCG) of Sacred Heart University, Connecticut.

Reprinted here with publisher permission. Journal of Group Theory 9.6 (2006): 799-808.

DOI

10.1515/JGT.2006.051

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