Geodesic
A note of a family of quasi-antiorders on semigroup
Kragujevac Journal of Mathematics, Tome 27 (2005) no. 1.

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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,=, ą ,·,s) be an ordered semigroup under an antiorder s. If S is a subdirect product of the ordered semigroup {Si: i Î I }, then there exists a family {si : i Î I} of quasi-antiorders on S which separates the elements of S. Conversely, if {si : i Î 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 Č(si)-1): i Î I }. 
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Daniel Abraham Romano. A note of a family of quasi-antiorders on semigroup. Kragujevac Journal of Mathematics, Tome 27 (2005) no. 1. http://geodesic.mathdoc.fr/item/KJM_2005_27_1_a1/