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 GF(p) for prime numbers p ≥ 5. Moreover, we prove that this set characterizes affine spaces over GF(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 GF(5).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-3,
author = {Jung R. Cho and J\'ozef Dudek},
title = {Affine spaces as models for regular identities},
journal = {Colloquium Mathematicae},
volume = {91},
year = {2002},
pages = {29-38},
zbl = {0992.03039},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-3}
}
Jung R. Cho; Józef Dudek. Affine spaces as models for regular identities. Colloquium Mathematicae, Tome 91 (2002) pp. 29-38. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm91-1-3/