Prime radicals of $\mathcal{K}$-ordered algebras as Kurosh radicals

The Kopytov's order for any algebras over a field is considered. Some results concerned with the properties of a factoralgebra for a lattice $\mathcal{K}$-ordered algebras and its $l$-prime radical are obtained. Also, some results concerned with the properties of ordered homomorphisms, strictly ordered homomorphisms and lattice homomorphisms of lattice ordered algebras are presented.