Following an idea of Grassmann's father, A1 also defined the exterior product, also called "combinatorial product" (in German: "äußeres Produkt" or "kombinatorisches Produkt"), the key operation of an algebra now called exterior algebra. (One should keep in mind that in Grassmann's day, the only axiomatic theory was Euclidean geometry, and the general notion of an abstract algebra had yet to be defined.) In 1878, William Kingdon Clifford joined this exterior algebra to William Rowan Hamilton's quaternions by replacing Grassmann's rule "epep" = 0 by the rule "epep" = 1. (For quaternions, we have the rule "i"2 = "j"2 = "k"2 = −1.) For more details, see Exterior algebra.