Affine spaces as models for regular identities

Volume 91 / 2002

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


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


  • Jung R. ChoDepartment of Mathematics
    Pusan National University
    Pusan 609-735, Korea
  • Józef DudekMathematical Institute
    University of Wrocław
    Pl. Grunwaldzki 2/4
    50-384 Wrocław, Poland

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