P. V. Protic' and N. Stevanovic'
Abel-Grassmann's bands

Abel-Grassmann's groupoids or shortly AG-groupoids have been considered in a number of papers, although under the different names. In some papers they are named LA-semigroups in others left invertive groupoids.

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 Abel-Grassmann's band.