Bipolygons and Multipolygons over Semigroups

摘要

In the paper, bipolygons (polygons over two semigroups) and multipolygons (polygons over several semigroups) for some classes of semigroups are studied. A complete description of bipolygons over two arbitrary groups is obtained. The structure of unitary multipolygons over a family of monoids (i.e., multipolygons on which the identity elements of the monoids act identically) is reduced to a unitary polygon over the discrete direct product of these monoids. The description of bipolygons over the semigroups of left and right zeros is also obtained.