  A left almost semigroup (LA-semigroup) or an Abel-Grassmann's groupoid
(AG-groupoid) is investigated in several papers. In this paper we have
discussed ideals in LA-semigroups. Specifically, we have shown that every ideal
in an LA-semigroup S with left identity e is prime if and only if it is
idempotent and the set of ideals of S is totally ordered under inclusion. We
have shown that an ideal of S is prime if and only if it is semiprime and
strongly irreducible. We have proved also that every ideal in a regular
LA-semigroup S is prime if and only if the set of ideals of S is totally
ordered under inclusion. We have proved in the end that every ideal in S is
prime if and only if it is strongly irreducible and the set of ideals of S form
a semilattice.
