  The states of the physical algebra, namely the algebra generated by the
operators involved in encoding and processing qubits, are considered instead of
those of the whole system-algebra. If the physical algebra commutes with the
interaction Hamiltonian, and the system Hamiltonian is the sum of arbitrary
terms either commuting with or belonging to the physical algebra, then its
states are decoherence free. One of the considered examples shows that, for a
uniform collective coupling to the environment, the smallest number of physical
qubits encoding a decoherence free logical qubit is reduced from four to three.
