A Kondo lattice Hamiltonian for arbitrary total angular momentum J is formulated using a pseudofermion representation and without addition of RKKY interaction terms. An Hartree-Fock treatment is applied, and both variational and Green's function methods are used to calculate physical quantities from the linearized Hamiltonian. The Kondo phase is represented by finite hybridization. Magnetic ordering is examined via ordering vectors, but coexistence with the Kondo phase is not allowed. Phase diagrams are produced in S=1/2 and J=3/2 with second-order transitions at Kondo-paramagnetic and magnetic-paramagnetic boundaries, and first order transitions between Kondo and magnetic phases. Various coupling strengths are explored. Magnetic phases found include antiferromagnetism, ferromagnetism, and spin-density wave ordering of both commensurate and incommensurate varieties. In S=1/2, the magnetic phase exhibits a spike in critical temperature at half-filling. In J=3/2, the Kondo phase is reentrant at weaker coupling but not at stronger coupling. / Physics