  We introduce the notion of a strong equivalence between graded algebras and
prove that any partially-strongly-graded algebra by a group $G$ is
strongly-graded-equivalent to the skew group algebra by a product partial
action of $G$. As to a more general idempotent graded algebra $B$, we point out
that the Cohen-Montgomery duality holds for $B$, and $B$ is graded-equivalent
to a global skew group algebra. We show that strongly-graded-equivalence
preserves strong gradings and is nicely related to Morita equivalence of
product partial actions. Furthermore, we prove that any product partial group
action $\alpha $ is globalizable up to Morita equivalence; if such a
globalization $\beta $ is minimal, then the skew group algebras by $\alpha $
and $\beta $ are graded-equivalent; moreover, $\beta $ is unique up to Morita
equivalence. Finally, we show that strongly-graded-equivalent
partially-strongly-graded algebras are stably isomorphic as graded algebras.
