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Theoretical studies are presented how the electric dipole moment (EDM) of theelectron in H-like ions in electrostatic storage rings can sensitively bedetermined. With the proposed experiments a new constraint of about $10^{-29}$e cm for the electron EDM can be established what is by an order of magnitudemore restrictive than the existing bounds. Experiments with H-like ions mayprovide a possibility to distinguish between the electron EDM effect and theeffect of P,T violating interaction between the atomic electron and thenucleus.

The electric dipole moment of an electron in H-like ions in an electrostatic storage ring