Intermediate Associativity

Abstract

In the theory of total operations the notion of associativity arose with the help of one simple identity. In contrast to what happens naturally in the theory of partial operations there is a certain condition which can be treated as a different realisation of the notion of associativity. They are not equivalent. In this case the development of the theory reveals that neither one of them is preferred above the others. It is quite clear that in the theory of partial operations it is important that there are not one but several conditions that put the notion of associativity into effect. This circumstance has been noted more than once (Rosen 1973, Ljapin 1979, 1981).