Small clones and the projection property
| dc.creator | Pouzet, Maurice | |
| dc.creator | Rosenberg, Ivo G. | |
| dc.date | 2007-05-10 | |
| dc.date.accessioned | 2026-07-07T08:00:43Z | |
| dc.date.available | 2026-07-07T08:00:43Z | |
| dc.description | In 1986, the second author classified the minimal clones on a finite universe into five types. We extend this classification to infinite universes and to multiclones. We show that every non-trivial clone contains a "small" clone of one of the five types. From it we deduce, in part, an earlier result, namely that if $\mathcal C$ is a clone on a universe $A$ with at least two elements, that contains all constant operations, then all binary idempotent operations are projections and some $m$-ary idempotent operation is not a projection some $m\geq 3$ if and only if there is a Boolean group $G$ on $A$ for which $\mathcal C$ is the set of all operations $f(x_1,..., x_n)$ of the form $a+\sum_{i\in I}x_i$ for $a\in A$ and $I\subseteq \{1,..., n\}$. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0705.1519 | |
| dc.identifier | http://arxiv.org/abs/0705.1519 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/128738 | |
| dc.subject | Logic | |
| dc.subject | Combinatorics | |
| dc.subject | 08A55, 08A62 | |
| dc.title | Small clones and the projection property | |
| dc.type | text |