Clones on a prime cardinality universe containing an affine essential operation

Rok, strany: 1995, 201 - 215

Let $p$ be an odd prime and let $δ$ denote the number of divisors of $p-1$. We show that there are at most $q2^pδ+2$ clones on $\boldkey p:=\{0,…, p 1\}$ containing at least one essential affine operation. These clones form the principal filter (in the lattice $\frak L$ of clones on $\boldkey p$) generated by the minimal clone (i.e., an atom of $\frak L$) of all idempotent affine operations. We determine this filter and show that each of its clones is finitely generated extending thus a result of Marchenkov $(p=3)$ and Csikós $(p=5)$. For every subset $J$ of $\boldkey p$ and the clone $K_J$ of all operations $f$ on $\boldkey p$ such that $f(j,…, j)=j$ for all $j\in J$, we give a canonical (or normal) representation for each $f\in K_J$.

ISO 690:

Rosenberg, I. 1995. Clones on a prime cardinality universe containing an affine essential operation. In Tatra Mountains Mathematical Publications, vol. 5, no.1, pp. 201-215. 1210-3195.

APA:

Rosenberg, I. (1995). Clones on a prime cardinality universe containing an affine essential operation. Tatra Mountains Mathematical Publications, 5(1), 201-215. 1210-3195.