A fuel cell having a solid electrolyte layer (12) forms together with two electrode layers (11, 13) a plate-like multiple layer system (1). The layers are applied by means of coating procedures to an open-pored, electrically conducting carrier structure (10) in the sequence anode (11), electrolyte (12) and cathode (13). This multiple layer system (1) has an outer edge which is exposed during a current generating operation of the fuel cell to an external environment (60) which contains molecular oxygen. The material of the carrier structure assumes an oxidized or a reduced state in thermodynamic equilibrium at the operating temperature of the fuel cell depending on the environment. The outer edge (16) of the multiple layer plate is covered over with an inert material. At the operating temperature of the fuel cell this edge covering (126) forms a barrier which inhibits or prevents the transport of molecular oxygen out of the external environment (60) into the carrier structure. The material is in particular YSZ, i.e. zirconium dioxide ZrO2 which is stabilized with yttrium oxide Y2O3.