... TechnologyXi’an 710055, China2Faculty of Science, The Chinese University of Hong Kong, Hong Kong, ChinaDedicated to Professor Do Long Van on the occasion of his 65thbirthdayReceived May 10, ... Shumtranslations (and also the set P (S) of all right translations) of the semigroupS forms a semigroup under the composition of mappings. By the translationalhull of S, we mean a subsemigroup Ω(S) consisting ... that the translational hull of a strongly righ t or left adequatesemigroup is still of the same type. Our r esult amplifies a well kno wn result of Fountainand Lawson on translational hull of...