P-Stable Polygons

Resumo

P-stable polygons are studied. It is proved that the property of being (P, s)-, (P, a)-, and (P, e)-stable for the class of all polygons over a monoid S is equivalent to S being a group. We describe the structure of (P, s)-, (P, a)-, and (P, e)-stable polygons _SA over a countable left zero monoid S and, under the condition that the set A \ SA is indiscernible, over a right zero monoid.