Abstract
We study into monoids S the class of all S-polygons over which is primitive normal, primitive connected, or additive, that is, the monoids S the theory of any S-polygon over which is primitive normal, primitive connected, or additive. It is proved that the class of all S-polygons is primitive normal iff S is a linearly ordered monoid, and that it is primitive connected iff S is a group. It is pointed out that there exists no monoid S with an additive class of all S-polygons.
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References
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Translated from Algebra i Logika, Vol. 45, No. 3, pp. 300–313, May–June, 2006.
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Stepanova, A.A. Primitive connected and additive theories of polygons. Algebr Logic 45, 172–179 (2006). https://doi.org/10.1007/s10469-006-0015-6
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DOI: https://doi.org/10.1007/s10469-006-0015-6