A hollow body rivet element for attachment to a component of sheet metal (280), said hollow body element having one of an at least substantially square external outline and an at least substantially rectangular external outline, having a first broad side (2) and a second broad side (3), the hollow body element having a hollow cylindrical projection (210) which projects beyond the second broad side (3), the hollow cylindrical projection being surrounded by a ring recess (212) in the second broad side, the hollow cylindrical projection having a substantially constant diameter from its distal end to the recess the ring recess including a portion having a surface substantially parallel with the second broad side and being bounded by a wall in the hollow body element, the wall merging into the second broad side, the hollow body element also having a hole (204) which extends from the first broad side (2) through the hollow cylindrical projection, a first axial portion of said hole having a thread cylinder or being sized for the formation of a thread cylinder and a second axial portion of the hole within the hollow cylindrical projection having no thread, the hollow cylindrical projection containing the second axial portion of the hole being designed as a rivet section that, prior to being deformed to form a rivet bead which clampingly receives the sheet metal component between itself and the wall of the ring recess, has no undercut at an outer surface of the hollow cylindrical projection, the second axial portion of the hole within the hollow cylindrical projection having an internal diameter greater than the first axial portion of the hole and greater than a maximum diameter of a thread cylinder formed in the first axial portion, wherein features (272) providing security against rotation are formed at least one of outwardly at the hollow cylindrical projection (210) and inwardly in the region of the ring recess (212) around the hollow cylindrical projection (210) the features deviating radially from the otherwise substantially constant diameter of the cylindrical projection wherein the ring recess (212) is provided with a ring-like base region (238) which stands at least approximately in a plane parallel to the first and second broad sides (2, 3), merges at the radially inner side with an at least substantially rounded transition (240) into the outer side of the hollow cylindrical projection and merges at the radially outer side into a conical surface (242).