  We study Morita equivalence and Morita duality for rings with local units. We
extend the Auslander's results on the theory of Morita equivalence and the
Azumaya-Morita duality theorem to rings with local units. As a consequence, we
give a version of Morita theorem and Azumaya-Morita duality theorem over rings
with local units in terms of their full subcategory of finitely generated
projective unitary modules and full subcategory of finitely generated injective
unitary modules.
