On $l$-prime radicals of lattice ordered algebras

The Kopytov order for any algebras over a field is considered. The purpose of this paper is to investigate a generalization of the concept of prime radical to lattice ordered algebras over partially ordered fields. Prime radicals of $l$-algebras over partially ordered and directed fields are described. Some results concerning properties of the lower weakly solvable $l$-radical of $l$-algebras are obtained. Necessary and sufficient conditions for the $l$-prime radical of an $l$-algebra to be equal to the lower weakly solvable $l$-radical of an $l$-algebra are presented.