Chúng tôi chứng minh rằng thân tịnh của một nửa nhóm đủ mạnh mẽ bên phải hoặc trái là cùng loại. Kết quả của chúng tôi khuếch đại một kết quả nổi tiếng của Fountain và Lawson thân tịnh của một nửa nhóm đầy đủ được đưa ra vào năm 1985. 2000 Toán Phân loại Chủ đề. | Vietnam Journal of Mathematics 34 4 2006 441-447 Viet n a m J o u r n a I of MATHEMATICS VAST 2006 The Translational Hull of a Strongly Right or Left Adequate Semigroup X. M. Ren1 and K. P. Shum2 yDept. of Mathematics Xi an University of Architecture and Technology Xi an 710055 China 2 Faculty of Science The Chinese University of Hong Kong Hong Kong China .th. Received May 10 2005 Revised October 5 2006 Abstract. We prove that the translational hull of a strongly right or left adequate semigroup is still of the same type. Our result amplifies a well known result of Fountain and Lawson on translational hull of an adequate semigroup given in 1985. 2000 Mathematics Subject Classification 20M10. Keywords Translational hulls right adequate semigroups strongly right adequate semigroups. 1. Introduction . S . S Thls research is supported by the National Natural Science Foundation of China Grant No. 10671151 the NSF grant of Shaanxi Province grant No. 2004A10 and the SF grant of Education Commission of Shaanxi Province grant No. 05JK240 P. R. China. This research is partially supported by a RGC CUHK direct grant No. 2060297 2005 2006 . 442 X. M. Ren and . Shum . . .1 . a strongly right adequate semigroup. . .a strongly left adequate semigroup 2. Preliminaries idempotent balanced Lemma . Let be an idempotent balanced semigroup. Then the following statements hold If 1 and 2 are left translations of then 1 2 if and only if 1 2 for all . If 1 and 2 are right translations of then 1 2 if and only if 1 2 for all . Proof. Translational Hull of a Strongly Right or Left Adequate Semigroup 443 1 1 1 2 2 2 .1 2 Lemma . Let be an idempotent balanced semigroup. If ị. for. then the following statements are equivalent .1 1 2 2 .1 2 .1 2. Proof. 1 2 1 1 1 2 2 2 1 1 2 2 2 1 2 g 1 2 2 2 1 2 1 2 1 1 2 2 Lemma . If is a strongly right left adequate semigroup then every -class -class of contains a unique idempotent of . . . Lemma . Let be elements of a strongly right adequate .
