Kragujevac J. Math. 27 - 2 Kragujevac J. Math. 27 (2005) 11-18.

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 }.