  We present the inclusive invariant-mass, transverse momentum and rapidity
distributions of dielectrons (e$^{+}$e$^{-}$ pairs) in p+p interactions at 3.5
GeV beam kinetic energy. In the vector-meson mass region, a distinct peak
corresponding to direct $\omega$ decays is reconstructed with 2% mass
resolution. The data is compared to predictions from three model calculations.
Due to the large acceptance of the HADES apparatus for $e^{+}e^{-}$ invariant
masses above 0.2 GeV/$c^{2}$ and for transverse pair momenta p$_{t}$ $ <$ 1
GeV/$c$, acceptance corrections are to a large extent model independent. This
allows us to extract from dielectron data for the first time at this energy the
inclusive production cross sections for light vector mesons. Inclusive
production cross sections for $\pi^o$ and $\eta$ mesons are also reported. The
obtained results will serve as an important reference for the study of vector
meson production in proton-nucleus and heavy-ion collisions. Furthermore, using
this data, an improved value for the upper bound of the branching ratio for
direct $\eta$ decays into the electron-positron channel is obtained.
