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Abstract
It is known that for a strong Dubreil-Jacotin semigroup the propeq of being perfect is equivalent to that of being naturally ordered. Here we consider the existence of a smallest idempotent and the analogous notion of being dually perfect, whch we show is not equivalent to being dually naturally ordered. The main objective of the paper is to obtain a suucture theorem for dually perfect orthodox Dubreil-Jacotinsemigroups on which Green's relations are regular.
1Support from the junta Nacional de investigacão Cientifice Tecnoloógica of Portugal is gratefully acknowledged
2NATO Collaborative Research Grant 910765 is gratefully acknowledged
1Support from the junta Nacional de investigacão Cientifice Tecnoloógica of Portugal is gratefully acknowledged
2NATO Collaborative Research Grant 910765 is gratefully acknowledged
Notes
1Support from the junta Nacional de investigacão Cientifice Tecnoloógica of Portugal is gratefully acknowledged
2NATO Collaborative Research Grant 910765 is gratefully acknowledged