Abstract. Alternative algebras known as comtrans algebras have been used in the coordinatization of web structures, and in the formulation of quantum mechanics. Time reversal in quantum mechanics corresponds to transposition of comtrans algebras. The current paper presents an alternative axiomatization of comtrans algebras, namely as tercom algebras, that simplifies the description of transposition. A new class of simple comtrans or tercom algebras, corresponding to simple alternative Akivis algebras, is then obtained.

AMS Subject Classification (1991): 17D10, 17D99, 53A60

Received December 28, 1994 and in revised form November 17, 1995. (Registered under 5714/2009.)