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,=, ¹ ,·,s) be an ordered semigroup under an antiorder
s. If S is a subdirect product of the ordered semigroup
{S_{i}: i Î I }, then there exists a family {s_{i} : i Î I} of quasi-antiorders on S which separates the elements of
S. Conversely, if {s_{i} : 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 / (s_{i} È(s_{i})^{-1}): i Î I }.