Algebraic form of a theorem of Hahn—Banach type for lattice manifolds

Let E be a vector lattice. A linear functionalf on E is called a lattice homomorphism iff(sup (x, y)) = max (f(x),f(y)) for all x, y E. For lattice homomorphisms a theorem of Hahn—Banach type is valid. In this note we prove an algebraic analog of this theorem.Translated from Matematicheskie Zametki, Vol. 16, No. 4, pp. 595–600, October, 1974.In conclusion the author expresses his thanks to D. A. Raikov for his statement of the problem and his interest in my work.