Regular polygons with primitive connected theories

A. A. Stepanova<sup>ab

a</sup> Far Eastern Federal University, Vladivostok, Russia
^b Institute of Applied Mathematics, Vladivostok, Russia

Abstract: We study the monoids $S$ over which the class of all regular $S$-polygons is axiomatizable and primitive connected. We prove that the axiomatizable class of all regular $S$-polygons is primitive connected if and only if the semigroup $R$ is a rectangular band of groups and $R=eR$ for some idempotent $e\in R$, where $_SR$ is the inclusion maximal regular subpolygon in the $S$-polygon $_SS$.

Keywords: primitive normal theory, primitive connected theory, polygon, regular polygon.

UDC: 510.67+512.56

Received: 24.04.2013

 English version: Siberian Mathematical Journal, 2014, 55:3, 544–547

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