TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The coating of the formation of lithium dendrites is reduced or prevented to or on the negative electrode, where the coating comprises at least partially an inorganic ion-conductive material. The coating at least partially comprises ceramic material, which has at least one compound including oxides, phosphates, sulfates, titanates, silicates, alumino-silicates having at least one of the elements including zirconium, aluminum and/or lithium. The coating is at least partially cohesively connected with the surface of the negative electrode. The coating is arranged at least partially between the negative electrode and separator. The positive electrode at least partially comprises at least one electrochemically active material including: at least one lithium metal phosphate compound of formula (LiMPO4); at least one lithium metal or lithium metal oxide in the spinel-type, where the metal is cobalt, manganese or nickel; or at least one lithium metal or lithium metal oxide in a type which is different from the spinel type, where the metal is cobalt, manganese or nickel. The electrolyte is designed as a non-aqueous electrolyte which has an organic solvent and lithium ions, or an ionic liquid. The negative electrode at least partially contains elemental lithium or a lithium alloy.M = transition metal cation including Mn, Fe, Co and/or Ti.    TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Components: The separator is: a separator, which comprises at least one partially permeable support, which is not or only poorly electron-conductive, where the carrier is coated on at least one side with an inorganic material, and is used as at least partially fuel-permeable support, preferably as an organic material, which is formed as a non-woven fleece; a separator comprising a polyethylene terephthalate, a polyolefin, a polyetherimide, a polyamide, a polyacrylonitrile, a polycarbonate, a polysulfone, a polyethersulfone, polyvinylidene fluoride and/or a polystyrene; or a separator having an inorganic material. At least one electrode comprises an electrode support, which is coated at least partially by electrochemically active material. The electrode support is designed at least partly as a foil, mesh structure or fabric, which comprises a material including at least one metal or metal alloy, preferably copper, copper-containing alloy or aluminum, at least metal which is not capable of forming an alloy with lithium, and/or at least one plastic.    TECHNOLOGY FOCUS - POLYMERS - Preferred Components: The organic material is a polymer, preferably at least one polymer including polyethylene terephthalate, polyolefin, or polyetherimide. The organic material is coated with an inorganic, ion-conducting material, which is ionically conductive in a temperature of -40 degrees C to 200 degrees C, and inorganic, ion-conducting material comprises at least one compound including oxide, phosphate, silicate, titanate, sulfates, alumino-silicate with at least one of the elements including zirconium, aluminum, lithium, preferably zirconium oxide, where the inorganic material particles exhibit a maximum diameter of less than 100 nm.