Morita equivalence of partial group actions and globalization

We consider a large class of partial actions of groups on rings, called regular, which contains all s-algebras. For them the notion of Morita equivalence is introduced, and it is shown that any regular partial action is Morita equivalent to a globalizable one and that the globalization is essentially unique. It is also proved that Morita equivalent s-unital partial actions on commutative rings must be isomorphic, and an analogous result for -algebras is also established.