An adapter is provided for fastening a filter element in a cylindrical receiving opening of a bottom part of a lower piece of a filter housing. The adapter has at least one seal arranged in a peripheral groove on the circumference of the adapter to permit fluid-tight separation of a non-filtrate chamber, which surrounds the external jacket of the filter and from which medium to be filtered can be delivered to the filter, from a filtrate chamber into which the filtrate can be introduced from the filter. The seal is connected by injection molding to a base surface of the peripheral groove and is at a distance from at least one side wall delimiting the base surface of the groove.