  A novel effective Hamiltonian in the subspace of singly occupied states is
obtained by applying the Gutzwiller projection approach to a generalized
Hubbard model with the interactions between two nearest- neighbor sites. This
model provides a more complete description of the physics of strongly
correlated electron systems. The system is not necessarily in a ferromagnetic
state as temperature approaches zero at any doping level. The system, however,
must be in an antiferromagnetic state at the origin of the doping-temperature
plane. Moreover, the model exhibits superconductivity in a doped region at
sufficiently low temperatures. We summarize the studies and provide a phase
diagram of the antiferromagnetism and the superconductivity of the model in the
doping-temperature plane here. Details will be presented in subsequent papers.
