Abel-Grassmann's bands
Petar V. Proti · 2004
Abel-Grassmann’s groupoids or shortly AG-groupoids have been considered in a number of papers, although under the dierent names. In some papers they are named LA-semigroups [3] in others left invertive groupoids [2]. In this paper we deal with AG-bands, i.e., AG-groupoids whose all elements are idempotents. We introduce a few congruence relations on AG-band and consider decompositions of Abel-Grassmann’s bands induced by these congruences. We also give the natural partial order on AbelGrassmann’s band.