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On Abel-Grassmann’s groupoids. (English) Zbl 0880.20051
Kočinac, Ljubiša D. (ed.), Proceedings of the mathematical conference in Priština (YU), September 28 – October 1, 1994. Priština: Univ. of Priština, Faculty of Sciences, 31-38 (1995).

Summary: Abel-Grassmann groupoids (or in some papers LA-semigroups) are considered in a few papers. In those papers some elementary properties are given. We shall try here to collect all results which are archieved in studying this class of groupoids. Most of these results are due to the authors and they are not published yet. There are also a few results of other mathematicians.

In the first section we present some general properties of Abel-Grassmann groupoids, AG-test and describe ideals in AG-groupoids. In the second section we deal with AG-bands. Natural partial order relations on AG-bands will be given, as well as decomposition of AG-bands. The third section is devoted to AG * -groupoids. We give semilattice decomposition, natural partial order relation and structural theorem for this class of AG-groupoids. In the fourth section we describe AG * -groupoids. Natural partial order, semilattice decomposition and congruences on AG ** -groupoids will be described.

MSC:
20N02Sets with a single binary operation (groupoids)