Ideals in selfdistributive groupoids. (English) Zbl 0807.20058

Kepka, Tomáš

Commentat. Math. Univ. Carol. 35, No. 1, 187-191 (1994).

Let \(G\) be a left distributive groupoid. Denote by \(P(G)\) the groupoid of all subsets of \(G\), and by \(R(G)\) the subgroupoid of \(P(G)\) generated by the element \(G\). Some technical results are proved from which it follows that \(R(G)\) is a medial, left distributive groupoid which is linearly ordered by inclusion; this ordering is stable.

Reviewer: J.Ježek (Praha)

MSC:

20N02	Sets with a single binary operation (groupoids)
20M12	Ideal theory for semigroups

Keywords:

left distributive groupoids