Abstract. A finite algebra $\underline A=(A;F)$ is called preprimal if $\underline A$ is not primal (functionally complete) but for every operation $f$ defined on $A$ which is not a term operation of $\underline A$ the algebra $\underline A'=(A;A;F\cup\{f\} )$ is primal. Some of the preprimal algebras were determined by S. V. Jablonskij in the early sixties. I. G. Rosenberg gave a complete list in 1970. In this paper all varieties generated by single preprimal algebras, their dualities and category equivalences are studied. The most surprising result is that up to category equivalence the algebra of Jablonskij's "small" list represent all preprimal algebras.

AMS Subject Classification (1991): 08A40, 08C99, 18B99

Keyword(s): Finite algebra, preprimal

Received November 20, 1991 and in revised form February 5, 1993. (Registered under 5533/2009.)