A completion for partially ordered Abelian groups
type: Item
instance of: scholarly article
title: A completion for partially ordered Abelian groups
zbMATH Open document ID: 0541.06011
DOI: 10.1007/BF02572489
published in: Semigroup Forum
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134655
review text: The author describes a completion process for a partially ordered abelian group G, using non-empty subsets of G which are bounded above and closed in the Scott topology on G. This completion is compared with the more familiar Dedekind completion. The author's completion satisfies a universal property which makes it a left adjoint to the forgetful functor from the category of partially ordered abelian groups with order preserving (or reversing) Scott continuous group homomorphisms to the category of semicontinuous closed posets with semicontinuous functions.
Mathematics Subject Classification ID: 06F20
Mathematics Subject Classification ID: 06B23
Mathematics Subject Classification ID: 06F30
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 3859195
zbMATH Keywords: Scott topology
zbMATH Keywords: Dedekind completion
zbMATH Keywords: partially ordered abelian groups
zbMATH Keywords: semicontinuous closed posets
author: K. I. Rosenthal
MaRDI profile type: Publication
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OpenAlex ID: W2011486106
description: scientific article; zbMATH DE number 3859195