We present a precise measurement of the ratio R_K=B(Kto e u(gamma))/B(Kto mu u(gamma)) and a study of the radiative process $Kto e ugamma$, performed with the KLOE detector. The results are based on data collected at the Frascati $e^+e^-$ collider
DAFNE for an integrated luminosity of 2.2 fb$^{-1}$. We find R_K = (2.493pm0.025pm0.019)x10^{-5}$, in agreement with the Standard Model expectation. This result is used to improve constraints on parameters of the Minimal Supersymmetric Standard Model with lepton flavor violation. We also measured the differential decay rate $dGamma(Kto e ugamma)/dE_gamma$ for photon energies $10<E_gamma<250$ MeV. Results are compared with predictions from theory.
