  The Nakayama conjecture states that an algebra of infinite dominant dimension
should be self-injective. Motivated by understanding this conjecture in the
context of derived categories, we study dominant dimensions of algebras under
derived equivalences induced by tilting modules, specifically, the infinity of
dominant dimensions under tilting procedure. We first give a new method to
produce derived equivalences from relatively exact sequences, and then
establish relationships and lower bounds of dominant dimensions for derived
equivalences induced by tilting modules. Particularly, we show that under a
sufficient condition the infinity of dominant dimensions can be preserved by
tilting, and get not only a class of derived equivalences between two algebras
such that one of them is a Morita algebra in the sense of Kerner-Yamagata and
the other is not, but also the first counterexample to a question whether
generalized symmetric algebras are closed under derived equivalences.
