On generalizations of quasi-prime ideals of an ordered left almost semigroups

Abstract The purposes of this paper are to introduce generalizations quasi-prime ideals the context $$\phi $$ ? -quasi-prime ideals. Let : {\mathcal {I}}(S) \rightarrow \cup \left\{ \emptyset \right\} : I ( S ) ? ? ? be a function where {I}}(S)$$ is set all left an ordered $${{\mathcal {L}}}{{\mathcal {A}}}$$ L A -semigroup S . A proper ideal called ideal, if for each $$a, b\in S$$ a , b ? with $$ab \in - \phi (A)$$ - , then $$a A$$ or $$b\in Some characterizations and obtained. Moreover, we investigate relationships between weakly quasi-prime, almost $$\omega ? -quasi-prime, m -semigroups. Finally, obtain necessary sufficient conditions in order ideal.