## Affine spaces as models for regular identities

### Volume 91 / 2002

Colloquium Mathematicum 91 (2002), 29-38
MSC: 03C05, 08A40.
DOI: 10.4064/cm91-1-3

#### Abstract

In [7] and [8], two sets of regular identities without finite proper models were introduced. In this paper we show that deleting one identity from any of these sets, we obtain a set of regular identities whose models include all affine spaces over $\mathop {\rm GF}\nolimits (p)$ for prime numbers $p\geq 5$. Moreover, we prove that this set characterizes affine spaces over $\mathop {\rm GF}\nolimits (5)$ in the sense that each proper model of these regular identities has at least 13 ternary term functions and the number 13 is attained if and only if the model is equivalent to an affine space over $\mathop {\rm GF}\nolimits (5)$.