  The effect of the vector interaction on three flavor magnetized matter is
studied within the SU(3) Nambu--Jona-Lasiono quark model. We have considered
cold matter under a static external magnetic field within two different models
for the vector interaction in order to investigate how the form of the vector
interaction and the intensity of the magnetic field affect the equation of
state as well as the strangeness content. It was shown that the flavor
independent vector interaction predicts a smaller strangeness content and,
therefore, harder equations of state. On the other hand, the flavor dependent
vector interaction favors larger strangeness content the larger the vector
coupling. We have confirmed that at low densities the magnetic field and the
vector interaction have opposite competing effects: the first one softens the
equation of state while the second hardens it. Quark stars and hybrid stars
subject to an external magnetic field were also studied. Larger star masses are
obtained for the flavor independent vector interaction. Hybrid stars may bare a
core containing deconfined quarks if neither the vector interaction nor the
magnetic field are too strong. Also, the presence of strong magnetic fields
seems to disfavor the existence of a quark core in hybrid stars.
