Affine spaces as models for regular identities

Jung R. Cho¹ ; Józef Dudek²

¹ Department of Mathematics Pusan National University Pusan 609-735, Korea
² Mathematical Institute University of Wrocław Pl. Grunwaldzki 2/4 50-384 Wrocław, Poland

Colloquium Mathematicum, Tome 91 (2002) no. 1, pp. 29-38

Résumé

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 $\mathop {\rm GF}\nolimits (5)$.

Détail

DOI : 10.4064/cm91-1-3

Keywords: sets regular identities without finite proper models introduced paper deleting identity these sets obtain set regular identities whose models include affine spaces mathop nolimits prime numbers geq moreover prove set characterizes affine spaces mathop nolimits sense each proper model these regular identities has least ternary term functions number attained only model equivalent affine space mathop nolimits