# Fuzzy ideals extenstions of ordered semigroups

## (*Lobachevskii Journal of Mathematics, Volume XIX*)

In this paper, we introduce the concepts of
the extension of fuzzy ideals , prime, semiprime and 3-prime fuzzy
ideals in an ordered semigroup *S*, respectively. We discuss
properties of fuzzy ideals extensions and the relationships
between prime fuzzy ideals and 3-prime fuzzy ideals of *S*
in terms of the extension of fuzzy ideals of *S*,
we give an example to show that 3-prime fuzzy ideal is not
necessarily prime. Moreover, for commutative ordered semigroups,
we obtain some properties of the extension of fuzzy ideals in commutative
ordered
semigroup.