  We show that the term equivalence between MV-algebras and MV-semirings lifts
to involutive residuated lattices and a class of semirings called
\textit{involutive semirings}. The semiring perspective helps us find a
necessary and sufficient condition for the interval $[0,1]$ to be a subalgebra
of an involutive residuated lattice. We also import some results and techniques
of semimodule theory in the study of this class of semirings, generalizing
results about injective and projective MV-semimodules. Indeed, we note that the
involution plays a crucial role and that the results for MV-semirings are still
true for involutive semirings whenever the Mundici functor is not involved. In
particular, we prove that involution is a necessary and sufficient condition in
order for projective and injective semimodules to coincide.
