Jordan *-derivation pairs and quadratic functionals on modules over *-rings

Summary We give a new simple proof of Šemrl’s recent representation theorem for quasi-quadratic functions acting on unital modules and then show that our approach also gives a certain extension of Šemrl’s result. This paper is intended to point out the usefulness of the ternary point of view even when we are dealing with problems which involve only binary structure. Dedicated to the memory of Professor Gy?rgy Szabó Supported in part by the Slovene Ministry of Science grant P1-5505-0101/93.