Directoids and directed groups

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1995 English Publisher:Springer Science and Business Media LLCJournal:Algebra Universalis, volume 33, pages 254-273 (issn: 0002-5240, eissn: 1420-8911,

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Authors: Gardner, B. J.; Parmenter, M. M.;

doi: 10.1007/bf01190937

Directoids and directed groups

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Abstract

\textit{J. Ježek} and \textit{R. Quackenbush} [ibid. 27, No. 1, 49-69 (1990; Zbl 0699.08002)] have introduced directoids as groupoids corresponding exactly to up-directed posets (viz \(a \leq b\) iff \(ab = b\)). In this paper, this concept is further investigated, both in its own and in combination with an abelian group structure.

Related Organizations

Memorial University of Newfoundland
Canada
University of Tasmania
Australia

Keywords

up-directed posets, directoids, Ordered sets, Sets with a single binary operation (groupoids), Ordered abelian groups, Riesz groups, ordered linear spaces, directed partially ordered abelian group

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