Geodesic
A note of a family of quasi-antiorders on semigroup
Kragujevac Journal of Mathematics, Tome 27 (2005), p. 11 .

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A NOTE OF A FAMILY OF QUASI-ANTIORDERS ON SEMIGROUP Daniel Abraham Romano Faculty of Natural Sciences and Mathematics, 78000 Banja Luka, Bosnia and Herzegovina (e-mails: bato49@hotmail.com)(Received February 7, 2005) Abstract. Let (S,=, � ,·,s) be an ordered semigroup under an antiorder s. If S is a subdirect product of the ordered semigroup {Si: i � I }, then there exists a family {si : i � I} of quasi-antiorders on S which separates the elements of S. Conversely, if {si : i � I } is a family of quasi-antiorders on S which separates the elements if S, then S is a subdirect product of the ordered semigroups {S / (si �(si)-1): i � I }.
Classification : 03F65 06F05
Keywords: constructive algebra, antiorder, quasi-antiorder, isotone mapping, reverse isotone mapping, subdirect product, separation of elements of semigroup 
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Daniel Abraham Romano. A note of a family of quasi-antiorders on semigroup. Kragujevac Journal of Mathematics, Tome 27 (2005), p. 11 . http://geodesic.mathdoc.fr/item/KJM_2005_27_a1/