Directoids and directed groups. (English) Zbl 0832.06005

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

Algebra Univers. 33, No. 2, 254-273 (1995).

J. Ježek and 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.

Reviewer: J.Rosický (Brno)

MSC:

06A99	Ordered sets
20N02	Sets with a single binary operation (groupoids)
06F20	Ordered abelian groups, Riesz groups, ordered linear spaces

Keywords:

directed partially ordered abelian group; directoids; up-directed posets

Citations:

Zbl 0699.08002

References:

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